One possible concern with MRI (see Exercise 28) is turning

What is an induced current?

What is magnetic flux?

What is Lenzs law?

What is Faradays law?

What is an induced field?

How is electromagnetic induction used

A square conductor moves through a uniform magnetic field. Which of the figures shows the correct charge distribution on the conductor? v u v u v u v u (a) (b) (c) (d)

It is known that the earths magnetic field over northern Canada points straight down. The crew of a Boeing 747 aircraft flying at 260 m/s over northern Canada finds a 0.95 V potential difference between the wing tips. The wing span of a Boeing 747 is 65 m. What is the magnetic field strength there?

A metal bar of length l rotates with angular velocity v about a pivot at one end of the bar. A uniform magnetic field B u is perpendicular to the plane of rotation. What is the potential difference between the ends of the bar?

Is there an induced current in this circuit? If so, what is its direction?

FIGURE 30.8 shows a circuit consisting of a flashlight bulb, rated 3.0 V/1.5 W, and ideal wires with no resistance. The right wire of the circuit, which is 10 cm long, is pulled at constant speed v through a perpendicular magnetic field of strength 0.10 T. a. What speed must the wire have to light the bulb to full brightness? b. What force is needed to keep the wire moving?

A square loop of copper wire is pulled through a region of magnetic field. Rank in order, from strongest to weakest, the pulling forces F u a, F u b, F u c, and F u d that must be applied to keep the loop moving at constant speed.

FIGURE 30.14 is an edge view of a 10-cm-diameter circular loop in a uniform 0.050 T magnetic field. What is the magnetic flux through the loop?

A current-carrying wire is pulled away from a conducting loop in the direction shown. As the wire is moving, is there a cw current around the loop, a ccw current, or no current?

The 1.0 cm * 4.0 cm rectangular loop of FIGURE 30.16 is 1.0 cm away from a long, straight wire. The wire carries a current of 1.0 A. What is the magnetic flux through the loop?

A conducting loop is halfway into a magnetic field. Suppose the magnetic field begins to increase rapidly in strength. What happens to the loop? a. The loop is pushed upward, toward the top of the page. b. The loop is pushed downward, toward the bottom of the page. c. The loop is pulled to the left, into the magnetic field. d. The loop is pushed to the right, out of the magnetic field. e. The tension in the wires increases but the loop does not move.

FIGURE 30.22 shows two loops, one above the other. The upper loop has a battery and a switch that has been closed for a long time. How does the lower loop respond when the switch is opened in the upper loop?

The potential at a is higher than the potential at b. Which of the following statements about the inductor current I could be true? a. I is from a to b and steady. b. I is from a to b and increasing. c. I is from a to b and decreasing. d. I is from b to a and steady. e. I is from b to a and increasing. f. I is from b to a and decreasing

FIGURE 30.24 shows two coils wrapped side by side on a cylinder. When the switch for coil 1 is closed, does the induced current in coil 2 pass from right to left or from left to right through the current meter?

Rank in order, from largest to smallest, the time constants ta, tb, and tc of these three circuits.

A 2.0-cm-diameter loop of wire with a resistance of 0.010 is placed in the center of the solenoid seen in FIGURE 30.27a on the next page. The solenoid is 4.0 cm in diameter, 20 cm long, and wrapped with 1000 turns of wire. FIGURE 30.27b shows the current through the solenoid as a function of time as the solenoid is powered up. A positive current is defined to be cw when seen from the left. Find the current in the loop as a function of time and show the result as a graph.

The body is a conductor, so rapid magnetic field changes in an MRI machine can induce currents in the body. To estimate the size of these currents, and any biological hazard they might impose, consider the loop of muscle tissue shown in FIGURE 30.29. This might be muscle circling the bone of your arm or thigh. Although muscle is not a great conductorits resistivity is 1.5 mwe can consider it to be a conducting loop with a rather high resistance. Suppose the magnetic field along the axis of the loop drops from 1.6 T to 0 T in 0.30 s, which is about the largest possible rate of change for an MRI solenoid. What current will be induced?

A 4.0-cm-diameter solenoid is wound with 2000 turns per meter. The current through the solenoid oscillates at 60 Hz with an amplitude of 2.0 A. What is the maximum strength of the induced electric field inside the solenoid?

A coil with area 2.0 m2 rotates in a 0.010 T magnetic field at a frequency of 60 Hz. How many turns are needed to generate a peak voltage of 160 V?

An inductor is made by tightly wrapping 0.30-mm-diameter wire around a 4.0-mm-diameter cylinder. What length cylinder has an inductance of 10 mH?

A 1.0 A current passes through a 10 mH inductor coil. What potential difference is induced across the coil if the current drops to zero in 5.0 ms?

The 10 mH inductor of Example 30.12 was 5.7 cm long and 4.0 mm in diameter. Suppose it carries a 100 mA current. What are the energy stored in the inductor, the magnetic energy density, and the magnetic field strength?

You have a 1.0 mH inductor. What capacitor should you choose to make an oscillator with a frequency of 920 kHz? (This frequency is near the center of the AM radio band.)

The switch in FIGURE 30.47 has been in position a for a long time. It is changed to position b at t = 0 s. a. What is the current in the circuit at t = 5.0 ms? b. At what time has the current decayed to 1% of its initial value?

Induction heating uses induced currents to heat metal objects to high temperatures for applications such as surface hardening, brazing, or even melting. To illustrate the idea, consider a copper wire formed into a 4.0 cm * 4.0 cm square loop and placed in a magnetic fieldperpendicular to the plane of the loopthat oscillates with 0.010 T amplitude at a frequency of 1000 Hz. What is the wires initial temperature rise, in C/min?

What is the direction of the induced current in FIGURE Q30.1?

You want to insert a loop of copper wire between the two permanent magnets in FIGURE Q30.2. Is there an attractive magnetic force that tends to pull the loop in, like a magnet pulls on a paper clip? Or do you need to push the loop in against a repulsive force? Explain

A vertical, rectangular loop of copper wire is half in and half out of the horizontal magnetic field in FIGURE Q30.3. (The field is zero beneath the dashed line.) The loop is released and starts to fall. Is there a net magnetic force on the loop? If so, in which direction? Explain.

Does the loop of wire in FIGURE Q30.4 have a clockwise current, a counterclockwise current, or no current under the following circumstances? Explain. a. The magnetic field points out of the page and is increasing. b. The magnetic field points out of the page and is constant. c. The magnetic field points out of the page and is decreasing

The two loops of wire in FIGURE Q30.5 are stacked one above the other. Does the upper loop have a clockwise current, a counterclockwise current, or no current at the following times? Explain. a. Before the switch is closed. b. Immediately after the switch is closed. c. Long after the switch is closed. d. Immediately after the switch is reopened.

FIGURE Q30.6 shows a bar magnet being pushed toward a conducting loop from below, along the axis of the loop. a. What is the current direction in the loop? Explain. b. Is there a magnetic force on the loop? If so, in which direction? Explain. Hint: A current loop is a magnetic dipole. c. Is there a force on the magnet? If so, in which direction?

A bar magnet is pushed toward a loop of wire as shown in FIGURE Q30.7. Is there a current in the loop? If so, in which direction? If not, why not?

FIGURE Q30.8 shows a bar magnet, a coil of wire, and a current meter. Is the current through the meter right to left, left to right, or zero for the following circumstances? Explain. a. The magnet is inserted into the coil. b. The magnet is held at rest inside the coil. c. The magnet is withdrawn from the left side of the coil.

Is the magnetic field strength in FIGURE Q30.9 increasing, decreasing, or steady? Explain

An inductor with a 2.0 A current stores energy. At what current will the stored energy be twice as large?

a. Can you tell which of the inductors in FIGURE Q30.11 has the larger current through it? If so, which one? Explain. b. Can you tell through which inductor the current is changing more rapidly? If so, which one? Explain. c. If the current enters the inductor from the bottom, can you tell if the current is increasing, decreasing, or staying the same? If so, which? Explain.

An LC circuit oscillates at a frequency of 2000 Hz. What will the frequency be if the inductance is quadrupled?

Rank in order, from largest to smallest, the three time constants ta to tc for the three circuits in FIGURE Q30.13. Explain.

For the circuit of FIGURE Q30.14: a. What is the battery current immediately after the switch closes? Explain. b. What is the battery current after the switch has been closed a long time? Explain.

The earths magnetic field strength is 5.0 * 10-5 T. How fast would you have to drive your car to create a 1.0 V motional emf along your 1.0-m-tall radio antenna? Assume that the motion of the antenna is perpendicular to B u

A potential difference of 0.050 V is developed across the 10-cmlong wire of FIGURE EX30.2 as it moves through a magnetic field perpendicular to the page. What are the strength and direction (in or out) of the magnetic field?

A 10-cm-long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total resistance of the wire and rail is 0.20 . Pulling the wire at a steady speed of 4.0 m/s causes 4.0 W of power to be dissipated in the circuit. a. How big is the pulling force? b. What is the strength of the magnetic field?

What is the magnetic flux through the loop shown in FIGURE EX30.4?

FIGURE EX30.5 shows a 10 cm *10 cm square bent at a 90 angle. A uniform 0.050 T magnetic field points downward at a 45 angle. What is the magnetic flux through the loop?

An equilateral triangle 8.0 cm on a side is in a 5.0 mT uniform magnetic field. The magnetic flux through the triangle is 6.0mWb. What is the angle between the magnetic field and an axis perpendicular to the plane of the triangle?

What is the magnetic flux through the loop shown in FIGURE EX30.7?

FIGURE EX30.8 shows a 2.0-cm-diameter solenoid passing through the center of a 6.0-cm-diameter loop. The magnetic field inside the solenoid is 0.20 T. What is the magnetic flux through the loop when it is perpendicular to the solenoid and when it is tilted at a 60 angle?

There is a cw induced current in the conducting loop shown in FIGURE EX30.9. Is the magnetic field inside the loop increasing in strength, decreasing in strength, or steady?

A solenoid is wound as shown in FIGURE EX30.10. a. Is there an induced current as magnet 1 is moved away from the solenoid? If so, what is the current direction through resistor R? b. Is there an induced current as magnet 2 is moved away from the solenoid? If so, what is the current direction through resistor R?

The metal equilateral triangle in FIGURE EX30.11, 20 cm on each side, is halfway into a 0.10 T magnetic field. a. What is the magnetic flux through the triangle? b. If the magnetic field strength decreases, what is the direction of the induced current in the triangle?

The current in the solenoid of FIGURE EX30.12 is increasing. The solenoid is surrounded by a conducting loop. Is there a current in the loop? If so, is the loop current cw or ccw?

The loop in FIGURE EX30.13 is being pushed into the 0.20 T magnetic field at 50 m/s. The resistance of the loop is 0.10 . What are the direction and the magnitude of the current in the loop?

FIGURE EX30.14 shows a 10-cm-diameter loop in three different magnetic fields. The loops resistance is 0.20 . For each, what are the size and direction of the induced current?

The resistance of the loop in FIGURE EX30.15 is 0.20 . Is the magnetic field strength increasing or decreasing? At what rate 1T/s2?

A 1000-turn coil of wire 1.0 cm in diameter is in a magnetic field that increases from 0.10 T to 0.30 T in 10 ms. The axis of the coil is parallel to the field. What is the emf of the coil?

A 5.0-cm-diameter coil has 20 turns and a resistance of 0.50 . A magnetic field perpendicular to the coil is B = 0.020t + 0.010t 2 , where B is in tesla and t is in seconds. a. Find an expression for the induced current I1t2 as a function of time. b. Evaluate I at t = 5 s and t = 10 s.

FIGURE EX30.18 shows the current as a function of time through a 20-cm-long, 4.0-cm-diameter solenoid with 400 turns. Draw a graph of the induced electric field strength as a function of time at a point 1.0 cm from the axis of the solenoid.

The magnetic field in FIGURE EX30.19 is decreasing at the rate 0.10 T/s. What is the acceleration (magnitude and direction) of a proton initially at rest at points a to d?

The magnetic field inside a 5.0-cm-diameter solenoid is 2.0 T and decreasing at 4.0 T/s. What is the electric field strength inside the solenoid at a point (a) on the axis and (b) 2.0 cm from the axis?

Scientists studying an anomalous magnetic field find that it is inducing a circular electric field in a plane perpendicular to the magnetic field. The electric field strength 1.5 m from the center of the circle is 4.0 mV/m. At what rate is the magnetic field changing?

Electricity is distributed from electrical substations to neighborhoods at 15,000 V. This is a 60 Hz oscillating (AC) voltage. Neighborhood transformers, seen on utility poles, step this voltage down to the 120 V that is delivered to your house. a. How many turns does the primary coil on the transformer have if the secondary coil has 100 turns? b. No energy is lost in an ideal transformer, so the output power Pout from the secondary coil equals the input power Pin to the primary coil. Suppose a neighborhood transformer delivers 250 A at 120 V. What is the current in the 15,000 V line from the substation?

The charger for your electronic devices is a transformer. Suppose a 60 Hz outlet voltage of 120 V needs to be reduced to a device voltage of 3.0 V. The side of the transformer attached to the electronic device has 60 turns of wire. How many turns are on the side that plugs into the outlet?

The maximum allowable potential difference across a 200 mH inductor is 400 V. You need to raise the current through the inductor from 1.0 A to 3.0 A. What is the minimum time you should allow for changing the current?

What is the potential difference across a 10 mH inductor if the current through the inductor drops from 150 mA to 50 mA in 10 ms? What is the direction of this potential difference? That is, does the potential increase or decrease along the direction of the current?

A 100 mH inductor whose windings have a resistance of 4.0 is connected across a 12 V battery having an internal resistance of 2.0 . How much energy is stored in the inductor?

How much energy is stored in a 3.0-cm-diameter, 12-cm-long solenoid that has 200 turns of wire and carries a current of 0.80 A?

MRI (magnetic resonance imaging) is a medical technique that produces detailed pictures of the interior of the body. The patient is placed into a solenoid that is 40 cm in diameter and 1.0 m long. A 100 A current creates a 5.0 T magnetic field inside the solenoid. To carry such a large current, the solenoid wires are cooled with liquid helium until they become superconducting (no electric resistance). a. How much magnetic energy is stored in the solenoid? Assume that the magnetic field is uniform within the solenoid and quickly drops to zero outside the solenoid. b. How many turns of wire does the solenoid have?

An FM radio station broadcasts at a frequency of 100 MHz. What inductance should be paired with a 10 pF capacitor to build a receiver circuit for this station?

A 2.0 mH inductor is connected in parallel with a variable capacitor. The capacitor can be varied from 100 pF to 200 pF. What is the range of oscillation frequencies for this circuit?

An MRI machine needs to detect signals that oscillate at very high frequencies. It does so with an LC circuit containing a 15 mH coil. To what value should the capacitance be set to detect a 450 MHz signal?

An LC circuit has a 10 mH inductor. The current has its maximum value of 0.60 A at t = 0 s. A short time later the capacitor reaches its maximum potential difference of 60 V. What is the value of the capacitance?

The switch in FIGURE EX30.33 has been in position 1 for a long time. It is changed to position 2 at t = 0 s. a. What is the maximum current through the inductor? b. What is the first time at which the current is maximum?

What value of resistor R gives the circuit in FIGURE EX30.34 a time constant of 25 ms?

At t = 0 s, the current in the circuit in FIGURE EX30.35 is I0. At what time is the current 1 2 I0?

The switch in FIGURE EX30.36 has been open for a long time. It is closed at t = 0 s. a. What is the current through the battery immediately after the switch is closed? b. What is the current through the battery after the switch has been closed a long time?

A 20 cm * 20 cm square loop has a resistance of 0.10 . A magnetic field perpendicular to the loop is B = 4t - 2t 2 , where B is in tesla and t is in seconds. What is the current in the loop at t = 0.0 s, t = 1.0 s, and t = 2.0 s?

A 100-turn, 2.0-cm-diameter coil is at rest with its axis vertical. A uniform magnetic field 60 away from vertical increases from 0.50 T to 1.50 T in 0.60 s. What is the induced emf in the coil?

A 100-turn, 8.0-cm-diameter coil is made of 0.50-mm-diameter copper wire. A magnetic field is parallel to the axis of the coil. At what rate must B increase to induce a 2.0 A current in the coil?

A circular loop made from a flexible, conducting wire is shrinking. Its radius as a function of time is r = r0e-bt . The loop is perpendicular to a steady, uniform magnetic field B. Find an expression for the induced emf in the loop at time t.

A 10 cm * 10 cm square loop lies in the xy-plane. The magnetic field in this region of space is B u = 10.30t ni + 0.50t 2 k n2 T, where t is in s. What is the emf induced in the loop at (a) t = 0.5 s and (b) t = 1.0 s?

A spherical balloon with a volume of 2.5 L is in a 45 mT uniform, vertical magnetic field. A horizontal elastic but conducting wire with 2.5 resistance circles the balloon at its equator. Suddenly the balloon starts expanding at 0.75 L/s. What is the current in the wire 2.0 s later?

A 3.0-cm-diameter, 10-turn coil of wire, located at z = 0 in the xy-plane, carries a current of 2.5 A. A 2.0-mm-diameter conducting loop with 2.0 * 10-4 resistance is also in the xyplane at the center of the coil. At t = 0 s, the loop begins to move along the z-axis with a constant speed of 75 m/s. What is the induced current in the conducting loop at t = 200ms? The diameter of the conducting loop is much smaller than that of the coil, so you can assume that the magnetic field through the loop is everywhere the on-axis field of the coil.

A 20 cm * 20 cm square loop of wire lies in the xy-plane with its bottom edge on the x-axis. The resistance of the loop is 0.50 . A magnetic field parallel to the z-axis is given by B = 0.80y2 t, where B is in tesla, y in meters, and t in seconds. What is the size of the induced current in the loop at t = 0.50 s?

A 2.0 cm * 2.0 cm square loop of wire with resistance 0.010 has one edge parallel to a long straight wire. The near edge of the loop is 1.0 cm from the wire. The current in the wire is increasing at the rate of 100 A/s. What is the current in the loop?

FIGURE P30.46 shows a 4.0-cm-diameter loop with resistance 0.10 around a 2.0-cm-diameter solenoid. The solenoid is 10 cm long, has 100 turns, and carries the current shown in the graph. A positive current is cw when seen from the left. Find the current in the loop at (a) t = 0.5 s, (b) t = 1.5 s, and (c) t = 2.5 s

FIGURE P30.47 shows a 1.0-cm-diameter loop with R = 0.50 inside a 2.0-cm-diameter solenoid. The solenoid is 8.0 cm long, has 120 turns, and carries the current shown in the graph. A positive current is cw when seen from the left. Determine the current in the loop at t = 0.010 s.

FIGURE P30.48 shows two 20-turn coils tightly wrapped on the same 2.0-cm-diameter cylinder with 1.0-mm-diameter wire. The current through coil 1 is shown in the graph. Determine the current in coil 2 at (a) t = 0.05 s and (b) t = 0.25 s. A positive current is into the page at the top of a loop. Assume that the magnetic field of coil 1 passes entirely through coil 2.

An electric generator has an 18-cm-diameter, 120-turn coil that rotates at 60 Hz in a uniform magnetic field that is perpendicular to the rotation axis. What magnetic field strength is needed to generate a peak voltage of 170 V?

A 40-turn, 4.0-cm-diameter coil with R = 0.40 surrounds a 3.0-cm-diameter solenoid. The solenoid is 20 cm long and has 200 turns. The 60 Hz current through the solenoid is I = I0 sin12pft2. What is I0 if the maximum induced current in the coil is 0.20 A?

A small, 2.0-mm-diameter circular loop with R = 0.020 is at the center of a large 100-mm-diameter circular loop. Both loops lie in the same plane. The current in the outer loop changes from +1.0 A to -1.0 A in 0.10 s. What is the induced current in the inner loop?

A rectangular metal loop with 0.050 resistance is placed next to one wire of the RC circuit shown in FIGURE P30.52. The capacitor is charged to 20 V with the polarity shown, then the switch is closed at t = 0 s. a. What is the direction of current in the loop for t 7 0 s? b. What is the current in the loop at t = 5.0 ms? Assume that only the circuit wire next to the loop is close enough to produce a significant magnetic field.

The square loop shown in FIGURE P30.53 moves into a 0.80 T magnetic field at a constant speed of 10 m/s. The loop has a resistance of 0.10 , and it enters the field at t = 0 s. a. Find the induced current in the loop as a function of time. Give your answer as a graph of I versus t from t = 0 s to t = 0.020 s. b. What is the maximum current? What is the position of the loop when the current is maximum?

The L-shaped conductor in FIGURE P30.54 moves at 10 m/s across and touches a stationary L-shaped conductor in a 0.10 T magnetic field. The two vertices overlap, so that the enclosed area is zero, at t = 0 s. The conductor has a resistance of 0.010 ohms per meter. a. What is the direction of the induced current? b. Find expressions for the induced emf and the induced current as functions of time. c. Evaluate E and I at t = 0.10 s.

A 20-cm-long, zero-resistance slide wire moves outward, on zero-resistance rails, at a steady speed of 10 m/s in a 0.10 T magnetic field. (See Figure 30.26.) On the opposite side, a 1.0 carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 50 mg. a. What is the induced current in the circuit? b. How much force is needed to pull the wire at this speed? c. If the wire is pulled for 10 s, what is the temperature increase of the carbon? The specific heat of carbon is 710 J/kgK.

Your camping buddy has an idea for a light to go inside your tent. He happens to have a powerful (and heavy!) horseshoe magnet that he bought at a surplus store. This magnet creates a 0.20 T field between two pole tips 10 cm apart. His idea is to build the hand-cranked generator shown in FIGURE P30.56. He thinks you can make enough current to fully light a 1.0 lightbulb rated at 4.0 W. Thats not super bright, but it should be plenty of light for routine activities in the tent. a. Find an expression for the induced current as a function of time if you turn the crank at frequency f. Assume that the semicircle is at its highest point at t = 0 s. b. With what frequency will you have to turn the crank for the maximum current to fully light the bulb? Is this feasible?

The 10-cm-wide, zero-resistance slide wire shown in FIGURE P30.57 is pushed toward the 2.0 resistor at a steady speed of 0.50 m/s. The magnetic field strength is 0.50 T. a. How big is the pushing force? b. How much power does the pushing force supply to the wire? c. What are the direction and magnitude of the induced current? d. How much power is dissipated in the resistor?

Youve decided to make the magnetic projectile launcher shown in FIGURE P30.58 for your science project. An aluminum bar of length l slides along metal rails through a magnetic field B. The switch closes at t = 0 s, while the bar is at rest, and a battery of emf Ebat starts a current flowing around the loop. The battery has internal resistance r. The resistances of the rails and the bar are effectively zero. a. Show that the bar reaches a terminal speed vterm, and find an expression for vterm. b. Evaluate vterm for Ebat = 1.0 V, r = 0.10 , l = 6.0 cm, and B = 0.50 T.

FIGURE P30.59 shows a U-shaped conducting rail that is oriented vertically in a horizontal magnetic field. The rail has no electric resistance and does not move. A slide wire with mass m and resistance R can slide up and down without friction while maintaining electrical contact with the rail. The slide wire is released from rest. a. Show that the slide wire reaches a terminal speed vterm, and find an expression for vterm. b. Determine the value of vterm if l = 20 cm, m = 10 g, R = 0.10 , and B = 0.50 T.

Experiments to study vision often need to track the movements of a subjects eye. One way of doing so is to have the subject sit in a magnetic field while wearing special contact lenses with a coil of very fine wire circling the edge. A current is induced in the coil each time the subject rotates his eye. Consider the experiment of FIGURE P30.60 in which a 20-turn, 6.0-mm-diameter coil of wire circles the subjects cornea while a 1.0 T magnetic field is directed as shown. The subject begins by looking straight ahead. What emf is induced in the coil if the subject shifts his gaze by 5 in 0.20 s?

A 10-turn coil of wire having a diameter of 1.0 cm and a resistance of 0.20 is in a 1.0 mT magnetic field, with the coil oriented for maximum flux. The coil is connected to an uncharged 1.0 mF capacitor rather than to a current meter. The coil is quickly pulled out of the magnetic field. Afterward, what is the voltage across the capacitor? Hint: Use I = dq/dt to relate the net change of flux to the amount of charge that flows to the capacitor

The magnetic field at one place on the earths surface is 55 mT in strength and tilted 60 down from horizontal. A 200- turn coil having a diameter of 4.0 cm and a resistance of 2.0 is connected to a 1.0 mF capacitor rather than to a current meter. The coil is held in a horizontal plane and the capacitor is discharged. Then the coil is quickly rotated 180 so that the side that had been facing up is now facing down. Afterward, what is the voltage across the capacitor? See the Hint in Problem 61.

Equation 30.26 is an expression for the induced electric field inside a solenoid 1r 6 R2. Find an expression for the induced electric field outside a solenoid 1r 7 R2 in which the magnetic field is changing at the rate dB/dt.

A solenoid inductor has an emf of 0.20 V when the current through it changes at the rate 10.0 A/s. A steady current of 0.10 A produces a flux of 5.0 mWb per turn. How many turns does the inductor have?

One possible concern with MRI (see Exercise 28) is turning the magnetic field on or off too quickly. Bodily fluids are conductors, and a changing magnetic field could cause electric currents to flow through the patient. Suppose a typical patient has a maximum crosssection area of 0.060 m2 . What is the smallest time interval in which a 5.0 T magnetic field can be turned on or off if the induced emf around the patients body must be kept to less than 0.10 V?

FIGURE P30.66 shows the current through a 10 mH inductor. Draw a graph showing the potential difference VL across the inductor for these 6 ms.

FIGURE P30.67 shows the potential difference across a 50 mH inductor. The current through the inductor at t = 0 s is 0.20 A. Draw a graph showing the current through the inductor from t = 0 s to t = 40 ms

A 3.6 mH inductor with negligible resistance has a 1.0 A current through it. The current starts to increase at t = 0 s, creating a constant 5.0 mV voltage across the inductor. How much charge passes through the inductor between t = 0 s and t = 5.0 s?

The current through inductance L is given by I = I0 sinvt. a. Find an expression for the potential difference VL across the inductor. b. The maximum voltage across the inductor is 0.20 V when L = 50 mH and f = 500 kHz. What is I0?

The current through inductance L is given by I = I0e-t/t . a. Find an expression for the potential difference VL across the inductor. b. Evaluate VL at t = 0, 1.0, and 3.0 ms if L = 20 mH, I0 = 50 mA, and t = 1.0 ms.

An LC circuit is built with a 20 mH inductor and an 8.0 pF capacitor. The capacitor voltage has its maximum value of 25 V at t = 0 s. a. How long is it until the capacitor is first fully discharged? b. What is the inductor current at that time?

An electric oscillator is made with a 0.10 mF capacitor and a 1.0 mH inductor. The capacitor is initially charged to 5.0 V. What is the maximum current through the inductor as the circuit oscillates?

For your final exam in electronics, youre asked to build an LC circuit that oscillates at 10 kHz. In addition, the maximum current must be 0.10 A and the maximum energy stored in the capacitor must be 1.0 * 10-5 J. What values of inductance and capacitance must you use

The inductor in FIGURE P30.74 is a 9.0-cm-long, 2.0-cmdiameter solenoid wrapped with 300 turns. What is the current in the circuit 10ms after the switch is moved from a to b?

The 300 mF capacitor in FIGURE P30.75 is initially charged to 100 V, the 1200 mF capacitor is uncharged, and the switches are both open. a. What is the maximum voltage to which you can charge the 1200 mF capacitor by the proper closing and opening of the two switches? b. How would you do it? Describe the sequence in which you would close and open switches and the times at which you would do so. The first switch is closed at t = 0 s.

The switch in FIGURE P30.76 has been open for a long time. It is closed at t = 0 s. What is the current through the 20 resistor a. Immediately after the switch is closed? b. After the switch has been closed a long time? c. Immediately after the switch is reopened?

The switch in FIGURE P30.77 has been open for a long time. It is closed at t = 0 s. a. After the switch has been closed for a long time, what is the current in the circuit? Call this current I0. b. Find an expression for the current I as a function of time. Write your expression in terms of I0, R, and L. c. Sketch a current-versus-time graph from t = 0 s until the current is no longer changing.

To determine the inductance of an unmarked inductor, you set up the circuit shown in FIGURE P30.78. After moving the switch from a to b at t = 0 s, you monitor the resistor voltage with an oscilloscope. Your data are shown in the table: Time (Ms) Voltage (V) 0 9.0 10 6.7 20 4.6 30 3.2 40 2.5 Use an appropriate graph of the data to determine the inductance

5.0ms after the switch of FIGURE P30.79 is moved from a to b, the magnetic energy stored in the inductor has decreased by half. What is the value of the inductance L?

The rectangular loop in FIGURE CP30.80 has 0.020 resistance. What is the induced current in the loop at this instant?

In recent years it has been possible to buy a 1.0 F capacitor. This is an enormously large amount of capacitance. Suppose you want to build a 1.0 Hz oscillator with a 1.0 F capacitor. You have a spool of 0.25-mm-diameter wire and a 4.0-cm-diameter plastic cylinder. How long must your inductor be if you wrap it with 2 layers of closely spaced turns?

The metal wire in FIGURE CP30.82 moves with speed v parallel to a straight wire that is carrying current I. The distance between the two wires is d. Find an expression for the potential difference between the two ends of the moving wire.

Lets look at the details of eddy-current braking. A square loop, length l on each side, is shot with velocity v0 into a uniform magnetic field B. The field is perpendicular to the plane of the loop. The loop has mass m and resistance R, and it enters the field at t = 0 s. Assume that the loop is moving to the right along the x-axis and that the field begins at x = 0 m. a. Find an expression for the loops velocity as a function of time as it enters the magnetic field. You can ignore gravity, and you can assume that the back edge of the loop has not entered the field. b. Calculate and draw a graph of v over the interval 0 s t 0.04 s for the case that v0 = 10 m/s, l = 10 cm, m = 1.0 g, R = 0.0010 , and B = 0.10 T. The back edge of the loop does not reach the field during this time interval.

An 8.0 cm * 8.0 cm square loop is halfway into a magnetic field perpendicular to the plane of the loop. The loops mass is 10 g and its resistance is 0.010 . A switch is closed at t = 0 s, causing the magnetic field to increase from 0 to 1.0 T in 0.010 s. a. What is the induced current in the square loop? b. With what speed is the loop kicked away from the magnetic field? Hint: What is the impulse on the loop?

A 2.0-cm-diameter solenoid is wrapped with 1000 turns per meter. 0.50 cm from the axis, the strength of an induced electric field is 5.0 * 10-4 V/m. What is the rate dI/dt with which the current through the solenoid is changing?

High-frequency signals are often transmitted along a coaxial cable, such as the one shown in FIGURE CP30.86. For example, the cable TV hookup coming into your home is a coaxial cable. The signal is carried on a wire of radius r1 while the outer conductor of radius r2 is grounded. A soft, flexible insulating material fills the space between them, and an insulating plastic coating goes around the outside. a. Find an expression for the inductance per meter of a coaxial cable. To do so, consider the flux through a rectangle of length l that spans the gap between the inner and outer conductors. b. Evaluate the inductance per meter of a cable having r1 = 0.50 mm and r2 = 3.0 mm.