A helium nucleus (charge _ 2e, mass _ 6.63 _ 10_27 kg)

A proton is released at the origin in a constant electric fi eld of 850 N/C acting in the positive x- direction. Find the change in the electric potential energy associated with the proton after it travels to x _ 2.5 m. (a) 3.4 _ 10_16 J (b) _3.4 _ 10_16 J (c) 2.5 _ 10_16 J (d) _2.5 _ 10_16 J (e) _1.6 _ 10_19 J

An electron in a TV picture tube is accelerated through a potential difference of 1.0 _ 104 V before it hits the screen. What is the kinetic energy of the electron in electron volts? (a) 1.0 _ 104 eV (b) 1.6 _ 1015 eV (c) 1.6 _ 1022 eV (d) 6.25 _ 1022 eV (e) 1.6 _ 1019 eV

A helium nucleus (charge _ 2e, mass _ 6.63 _ 10_27 kg) traveling at a speed of 6.20 _ 105 m/s enters an electric fi eld, traveling from point _, at a potential of 1.50 _ 103 V, to point _, at 4.00 _ 103 V. What is its speed at point _? (a) 7.91 _ 105 m/s (b) 3.78 _ 105 m/s (c) 2.13 _ 105 m/s (d) 2.52 _ 106 m/s (e) 3.01 _ 108 m/s

The electric potential at x _ 3.0 m is 120 V, and the electric potential at x _ 5.0 m is 190 V. What is the electric fi eld in this region, assuming its constant? (a) 140 N/C (b) _140 N/C (c) 35 N/C (d) _35 N/C (e) 75 N/C

An electronics technician wishes to construct a parallel- plate capacitor using rutile (k _ 1.00 _ 102) as the dielectric. If the cross-sectional area of the plates is 1.0 cm2, what is the capacitance if the rutile thickness is 1.0 mm? (a) 88.5 pF (b) 177.0 pF (c) 8.85 mF (d) 100.0 mF (e) 354 mF

Four point charges are positioned on the rim of a circle. The charge on each of the four is _0.5 mC, _1.5 mC, _1.0 mC, and _0.5 mC. If the electrical potential at the center of the circle due to the _0.5 mC charge alone is 4.5 _ 104 V, what is the total electric potential at the center due to the four charges? (a) 18.0 _ 104 V (b) 4.5 _ 104 V (c) 0 (d) _4.5 _ 104 V (e) 9.0 _ 104 V

If three unequal capacitors, initially uncharged, are connected in series across a battery, which of the following statements is true? (a) The equivalent capacitance is greater than any of the individual capacitances. (b) The largest voltage appears across the capacitor with the smallest capacitance. (c) The largest voltage appears across the capacitor with the largest capacitance. (d) The capacitor with the largest capacitance has the greatest charge. (e) The capacitor with the smallest capacitance has the smallest charge.

A parallel-plate capacitor is connected to a battery. What happens if the plate separation is doubled while the capacitor remains connected to the battery? (a) The stored energy remains the same. (b) The stored energy is doubled. (c) The stored energy decreases by a factor of 2. (d) The stored energy decreases by a factor of 4. (e) The stored energy increases by a factor of 4.

A parallel-plate capacitor fi lled with air carries a charge Q. The battery is disconnected, and a slab of material with dielectric constant k _ 2 is inserted between the plates. Which of the following statements is correct? (a) The voltage across the capacitor decreases by a factor of 2. (b) The voltage across the capacitor is doubled. (c) The charge on the plates is doubled. (d) The charge on the plates decreases by a factor of 2. (e) The electric fi eld is doubled.

After a parallel-plate capacitor is charged by a battery, it is disconnected from the battery and its plate separation is increased. Which of the following statements is correct? (a) The energy stored in the capacitor decreases. (b) The energy stored in the capacitor increases. (c) The electric fi eld between the plates decreases. (d) The potential difference between the plates decreases. (e) The charge on the plates decreases.

A battery is attached to several different capacitors connected in parallel. Which of the following statements is true? (a) All the capacitors have the same charge, and the equivalent capacitance is greater than the capacitance of any of the capacitors in the group. (b) The capacitor with the largest capacitance carries the smallest charge. (c) The potential difference across each capacitor is the same, and the equivalent capacitance is greater than any of the capacitors in the group. (d) The capacitor with the smallest capacitance carries the largest charge. (e) The potential differences across the capacitors are the same only if the capacitances are the same.

A battery is attached across several different capacitors connected in series. Which of the following statements are true? (a) All the capacitors have the same charge, and the equivalent capacitance is less than the capacitance of any of the individual capacitors in the group. (b) All the capacitors have the same charge, and the equivalent capacitance is greater than any of the individual capacitors in the group. (c) The capacitor with the largest capacitance carries the largest charge. (c) The potential difference across each capacitor must be the same. (d) The largest potential difference appears across the capacitor having the largest capacitance. (e) The largest potential difference appears across the capacitor with the smallest capacitance.

(a) Describe the motion of a proton after it is released from rest in a uniform electric fi eld. (b) Describe the changes (if any) in its kinetic energy and the electric potential energy associated with the proton.

Describe how you can increase the maximum operating voltage of a parallel-plate capacitor for a fi xed plate separation.

A parallel-plate capacitor is charged by a battery, and the battery is then disconnected from the capacitor. Because the charges on the capacitor plates are opposite in sign, they attract each other. Hence, it takes positive work to increase the plate separation. Show that the external work done when the plate separation is increased leads to an increase in the energy stored in the capacitor.

Distinguish between electric potential and electrical potential energy.

Suppose you are sitting in a car and a 20-kV power line drops across the car. Should you stay in the car or get out? The power line potential is 20 kV compared to the potential of the ground.

Why is it important to avoid sharp edges or points on conductors used in high-voltage equipment?

Explain why, under static conditions, all points in a conductor must be at the same electric potential.

If you are given three different capacitors C1, C2, and C3, how many different combinations of capacitance can you produce, using all capacitors in your circuits?

Why is it dangerous to touch the terminals of a highvoltage capacitor even after the voltage source that charged the battery is disconnected from the capacitor? What can be done to make the capacitor safe to handle after the voltage source has been removed?

The plates of a capacitor are connected to a battery. What happens to the charge on the plates if the connecting wires are removed from the battery? What happens to the charge if the wires are removed from the battery and connected to each other?

Can electric fi eld lines ever cross? Why or why not? Can equipotentials ever cross? Why or why not?

Is it always possible to reduce a combination of capacitors to one equivalent capacitor with the rules developed in this chapter? Explain.

If you were asked to design a capacitor for which a small size and a large capacitance were required, what factors would be important in your design?

Explain why a dielectric increases the maximum operating voltage of a capacitor even though the physical size of the capacitor doesnt change.

A uniform electric fi eld of magnitude 375 N/C pointing in the positive x-direction acts on an electron, which is initially at rest. After the electron has moved 3.20 cm, what is (a) the work done by the fi eld on the electron, (b) the change in potential energy associated with the electron, and (c) the velocity of the electron?

A uniform electric fi eld of magnitude 327 N/C is directed along the _y-axis. A 5.40-mC charge moves from the origin to the point (x, y) _ (_15.0 cm, _32.0 cm). (a) What is the change in the potential energy associated with this charge? (b) Through what potential difference did the charge move?

A potential difference of 90 mV exists between the inner and outer surfaces of a cell membrane. The inner surface is negative relative to the outer surface. How much work is required to eject a positive sodium ion (Na_) from the interior of the cell?

An ion accelerated through a potential difference of 60.0 V has its potential energy decreased by 1.92 _ 10_17 J. Calculate the charge on the ion.

The potential difference between the accelerating plates of a TV set is about 25 kV. If the distance between the plates is 1.5 cm, fi nd the magnitude of the uniform electric fi eld in the region between the plates.

To recharge a 12-V battery, a battery charger must move 3.6 _ 105 C of charge from the negative terminal to the positive terminal. How much work is done by the charger? Express your answer in joules.

Oppositely charged parallel plates are separated by 5.33 mm. A potential difference of 600 V exists between the plates. (a) What is the magnitude of the electric fi eld between the plates? (b) What is the magnitude of the force on an electron between the plates? (c) How much work must be done on the electron to move it to the negative plate if it is initially positioned 2.90 mm from the positive plate?

(a) Find the potential difference _Ve required to stop an electron (called a stopping potential) moving with an initial speed of 2.85 _ 107 m/s. (b) Would a proton traveling at the same speed require a greater or lesser magnitude potential difference? Explain. (c) Find a symbolic expression for the ratio of the proton stopping potential and the electron stopping potential, _Vp/_Ve. The answer should be in terms of the proton mass mp and electron mass me.

A 74.0-g block carrying a charge Q _ 35.0 mC is connected to a spring for which k _ 78.0 N/m. The block lies on a frictionless, horizontal surface and is immersed in a uniform electric fi eld of magnitude E _ 4.86 _ 104 N/C directed as shown in Figure P16.9. If the block is released from rest when the spring is unstretched (x _ 0), (a) by what maximum distance does the block move from its initial position? (b) Find the subsequent equilibrium position of the block and the amplitude of its motion. (c) Using conservation of energy, fi nd a symbolic relationship giving the potential difference between its initial position and the point of maximum extension in terms of the spring constant k, the amplitude A, and the charge Q.

On planet Tehar, the free-fall acceleration is the same as that on the Earth, but there is also a strong downward electric fi eld that is uniform close to the planets surface. A 2.00-kg ball having a charge of 5.00 mC is thrown upward at a speed of 20.1 m/s. It hits the ground after an interval of 4.10 s. What is the potential difference between the starting point and the top point of the trajectory?

An electron is at the origin. (a) Calculate the electric potential VA at point A, x _ 0.250 cm. (b) Calculate the electric potential VB at point B, x _ 0.750 cm. What is the potential difference VB _ VA? (c) Would a negatively charged particle placed at point A necessarily go through this same potential difference upon reaching point B? Explain.

Two point charges are on the y-axis. A 4.50-mC charge is located at y _ 1.25 cm, and a _2.24-mC charge is located at y _ _1.80 cm. Find the total electric potential at (a) the origin and (b) the point having coordinates (1.50 cm, 0).

(a) Find the electric potential, taking zero at infi nity, at the upper right corner (the corner without a charge) of the rectangle in Figure P16.13. (b) Repeat if the 2.00-mC charge is replaced with a charge of _2.00 mC.

Three charges are situated at corners of a rectangle as in Figure P16.13. How much energy would be expended in moving the 8.00-mC charge to infi nity?

Two point charges Q1 _ _5.00 nC and Q 2 _ _3.00 nC are separated by 35.0 cm. (a) What is the electric potential at a point midway between the charges? (b) What is the potential energy of the pair of charges? What is the signifi cance of the algebraic sign of your answer?

A point charge of 9.00 _ 10_9 C is located at the origin. How much work is required to bring a positive charge of 3.00 _ 10_9 C from infi nity to the location x _ 30.0 cm?

The three charges in Figure P16.17 are at the vertices of an isosceles triangle. Let q _ 7.00 nC and calculate the electric potential at the midpoint of the base.

An electron starts from rest 3.00 cm from the center of a uniformly charged sphere of radius 2.00 cm. If the sphere carries a total charge of 1.00 _ 10_9 C, how fast will the electron be moving when it reaches the surface of the sphere?

A proton is located at the origin, and a second proton is located on the x-axis at x _ 6.00 fm (1 fm _ 10_15 m). (a) Calculate the electric potential energy associated with this confi guration. (b) An alpha particle (charge _ 2e, mass _ 6.64 _ 10_27 kg) is now placed at (x, y) _ (3.00, 3.00) fm. Calculate the electric potential energy associated with this confi guration. (c) Starting with the threeparticle system, fi nd the change in electric potential energy if the alpha particle is allowed to escape to infi nity while the two protons remain fi xed in place. (Throughout, neglect any radiation effects.) (d) Use conservation of energy to calculate the speed of the alpha particle at infi nity. (e) If the two protons are released from rest and the alpha particle remains fi xed, calculate the speed of the protons at infi nity.

A proton and an alpha particle (charge _ 2e, mass _ 6.64 _ 10_27 kg) are initially at rest, separated by 4.00 _ 10_15 m. (a) If they are both released simultaneously, explain why you cant fi nd their velocities at infi nity using only conservation of energy. (b) What other conservation law can be applied in this case? (c) Find the speeds of the proton and alpha particle, respectively, at infi nity.

A small spherical object carries a charge of 8.00 nC. At what distance from the center of the object is the potential equal to 100 V? 50.0 V? 25.0 V? Is the spacing of the equipotentials proportional to the change in voltage?

Starting with the defi nition of work, prove that the local electric fi eld must be everywhere perpendicular to a surface having the same potential at every point.

In Rutherfords famous scattering experiments that led to the planetary model of the atom, alpha particles (having charges of _2e and masses of 6.64 _ 10_27 kg) were fi red toward a gold nucleus with charge _79e. An alpha particle, initially very far from the gold nucleus, is fi red at 2.00 _ 107 m/s directly toward the nucleus, as in Figure P16.23. How close does the alpha particle get to the gold nucleus before turning around? Assume the gold nucleus remains stationary.

Four point charges each having charge Q are located at the corners of a square having sides of length a. Find symbolic expressions for (a) the total electric potential at the center of the square due to the four charges and (b) the work required to bring a fi fth charge q from infi nity to the center of the square.

Consider the Earth and a cloud layer 800 m above the planet to be the plates of a parallel-plate capacitor. (a) If the cloud layer has an area of 1.0 km2 _ 1.0 _ 106 m2, what is the capacitance? (b) If an electric fi eld strength greater than 3.0 _ 106 N/C causes the air to break down and conduct charge (lightning), what is the maximum charge the cloud can hold?

(a) When a 9.00-V battery is connected to the plates of a capacitor, it stores a charge of 27.0 mC. What is the value of the capacitance? (b) If the same capacitor is connected to a 12.0-V battery, what charge is stored?

An air-fi lled parallel-plate capacitor has plates of area 2.30 cm2 separated by 1.50 mm. The capacitor is connected to a 12.0-V battery. (a) Find the value of its capacitance. (b) What is the charge on the capacitor? (c) What is the magnitude of the uniform electric fi eld between the plates?

(a) How much charge is on each plate of a 4.00-mF capacitor when it is connected to a 12.0-V battery? (b) If this same capacitor is connected to a 1.50-V battery, what charge is stored?

An air-fi lled capacitor consists of two parallel plates, each with an area of 7.60 cm2 and separated by a distance of 1.80 mm. If a 20.0-V potential difference is applied to these plates, calculate (a) the electric fi eld between the plates, (b) the capacitance, and (c) the charge on each plate.

A 1-megabit computer memory chip contains many 60.0 _ 10_15-F capacitors. Each capacitor has a plate area of 21.0 _ 10_12 m2. Determine the plate separation of such a capacitor. (Assume a parallel-plate confi guration.) The diameter of an atom is on the order of 10_10 m _ 1 . Express the plate separation in angstroms.

A parallel-plate capacitor with area 0.200 m2 and plate separation of 3.00 mm is connected to a 6.00-V battery. (a) What is the capacitance? (b) How much charge is stored on the plates? (c) What is the electric fi eld between the plates? (d) Find the magnitude of the charge density on each plate. (e) Without disconnecting the battery, the plates are moved farther apart. Qualitatively, what happens to each of the previous answers?

A small object with a mass of 350 mg carries a charge of 30.0 nC and is suspended by a thread between the vertical plates of a parallel-plate capacitor. The plates are separated by 4.00 cm. If the thread makes an angle of 15.0 with the vertical, what is the potential difference between the plates?

Given a 2.50-mF capacitor, a 6.25-mF capacitor, and a 6.00-V battery, fi nd the charge on each capacitor if you connect them (a) in series across the battery and (b) in parallel across the battery.

Find the equivalent capacitance of a 4.20-mF capacitor and an 8.50-mF capacitor when they are connected (a) in series and (b) in parallel.

Find (a) the equivalent capacitance of the capacitors in Figure P16.35, (b) the charge on each capacitor, and (c) the potential difference across each capacitor.

Find the charge on each of the capacitors in Figure

Two capacitors give an equivalent capacitance of 9.00 pF when connected in parallel and an equivalent capacitance of 2.00 pF when connected in series. What is the capacitance of each capacitor?

For the system of capacitors shown in Figure P16.37, fi nd (a) the equivalent capacitance of the system, (b) the charge on each capacitor, and (c) the potential difference across each capacitor.

Consider the combination of capacitors in Figure P16.38. (a) Find the equivalent single capacitance of the two capacitors in series and redraw the diagram (called diagram 1) with this equivalent capacitance. (b) In diagram 1 fi nd the equivalent capacitance of the three capacitors in parallel and redraw the diagram as a single battery and single capacitor in a loop. (c) Compute the charge on the single equivalent capacitor. (d) Returning to diagram 1, compute the charge on each individual capacitor. Does the sum agree with the value found in part (c)? (e) What is the charge on the 24.0-mF capacitor and on the 8.00-mF capacitor? (f) Compute the voltage drop across the 24.0-mF capacitor and (g) the 8.00-mF capacitor.

A 10.0-mF capacitor is fully charged across a 12.0-V battery. The capacitor is then disconnected from the battery and connected across an initially uncharged capacitor with capacitance C. The resulting voltage across each capacitor is 3.00 V. What is the value of C?

A 25.0-mF capacitor and a 40.0-mF capacitor are charged by being connected across separate 50.0-V batteries. (a) Determine the resulting charge on each capacitor. (b) The capacitors are then disconnected from their batteries and connected to each other, with each negative plate connected to the other positive plate. What is the fi nal charge of each capacitor, and what is the fi nal potential difference across the 40.0-mF capacitor?

(a) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P16.42 if C1 _ 5.00 mF, C2 _ 10.00 mF, and C3 _ 2.00 mF. (b) If the potential between points a and b is 60.0 V, what charge is stored on C3?

A 1.00-mF capacitor is charged by being connected across a 10.0-V battery. It is then disconnected from the battery and connected across an uncharged 2.00-mF capacitor. Determine the resulting charge on each capacitor.

Find the equivalent capacitance between points a and b in the combination of capacitors shown in Figure P16.44.

A 12.0-V battery is connected to a 4.50-mF capacitor. How much energy is stored in the capacitor?

Two capacitors, C1 _ 18.0 mF and C2 _ 36.0 mF, are connected in series, and a 12.0-V battery is connected across them. (a) Find the equivalent capacitance, and the energy contained in this equivalent capacitor. (b) Find the energy stored in each individual capacitor. Show that the sum of these two energies is the same as the energy found in part (a). Will this equality always be true, or does it depend on the number of capacitors and their capacitances? (c) If the same capacitors were connected in parallel, what potential difference would be required across them so that the combination stores the same energy as in part (a)? Which capacitor stores more energy in this situation, C1 or C2?

A parallel-plate capacitor has capacitance 3.00 mF. (a) How much energy is stored in the capacitor if it is connected to a 6.00-V battery? (b) If the battery is disconnected and the distance between the charged plates doubled, what is the energy stored? (c) The battery is subsequently reattached to the capacitor, but the plate separation remains as in part (b). How much energy is stored? (Answer each part in microjoules.)

A certain storm cloud has a potential difference of 1.00 _ 108 V relative to a tree. If, during a lightning storm, 50.0 C of charge is transferred through this potential difference and 1.00% of the energy is absorbed by the tree, how much water (sap in the tree) initially at 30.0C can be boiled away? Water has a specifi c heat of 4 186 J/kgC, a boiling point of 100C, and a heat of vaporization of 2.26 _ 106 J/kg.

The voltage across an air-fi lled parallel-plate capacitor is measured to be 85.0 V. When a dielectric is inserted and completely fi lls the space between the plates as in Figure 16.24, the voltage drops to 25.0 V. (a) What is the dielectric constant of the inserted material? Can you identify the dielectric? (b) If the dielectric doesnt completely fi ll the space between the plates, what could you conclude about the voltage across the plates?

A parallel-plate capacitor in air has a plate separation of 1.50 cm and a plate area of 25.0 cm2. The plates are charged to a potential difference of 2.50 _ 102 V and disconnected from the source. The capacitor is then immersed in distilled water. Determine (a) the charge on the plates before and after immersion, (b) the capacitance and potential difference after immersion, and (c) the change in energy stored in the capacitor due to immersion. Assume the distilled water is an insulator.

Determine (a) the capacitance and (b) the maximum voltage that can be applied to a Tefl on-fi lled parallel-plate capacitor having a plate area of 175 cm2 and an insulation thickness of 0.040 0 mm.

A commercial capacitor is constructed as in Figure 16.26a. This particular capacitor is made from a strip of aluminum foil separated by two strips of paraffi n-coated paper. Each strip of foil and paper is 7.00 cm wide. The foil is 0.004 00 mm thick, and the paper is 0.025 0 mm thick and has a dielectric constant of 3.70. What length should the strips be if a capacitance of 9.50 _ 10_8 F is desired before the capacitor is rolled up? (Use the parallel-plate formula. Adding a second strip of paper and rolling up the capacitor doubles its capacitance by allowing both surfaces of each strip of foil to store charge.)

A model of a red blood cell portrays the cell as a shperical capacitor, a positively charged liquid sphere of surface area A separated from the surrounding negatively charged fl uid by a membrane of thickness t. Tiny electrodes introduced into the interior of the cell show a potential difference of 100 mV across the membrane. The membranes thickness is estimated to be 100 nm and has a dielectric constant of 5.00. (a) If an average red blood cell has a mass of 1.00 _ 10_12 kg, estimate the volume of the cell and thus fi nd its surface area. The density of blood is 1 100 kg/m3. (b) Estimate the capacitance of the cell by assuming the membrane surfaces act as parallel plates. (c) Calculate the charge on the surface of the membrane. How many electronic charges does the surface charge represent? ADDITIONAL PROBLEMS

Three parallel-plate capacitors are constructed, each having the same plate spacing d and with C1 having plate area A1, C2 having area A2, and C3 having area A3. Show that the total capacitance C of the three capacitors connected in parallel is the same as that of a capacitor having plate spacing d and plate area A _ A1 _ A2 _ A3.

Three parallel-plate capacitors are constructed, each having the same plate area A and with C1 having plate spacing d1, C2 having plate spacing d2, and C3 having plate spacing d3. Show that the total capacitance C of the three capacitors connected in series is the same as a capacitor of plate area A and with plate spacing d _ d1 _ d2 _ d3.

For the system of four capacitors shown in Figure P16.37, fi nd (a) the total energy stored in the system and (b) the energy stored by each capacitor. (c) Compare the sum of the answers in part (b) with your result to part (a) and explain your observation.

A parallel-plate capacitor with a plate separation d has a capacitance C0 in the absence of a dielectric. A slab of dielectric material of dielectric constant k and thickness d/3 is then inserted between the plates as in Figure P16.57. Show that the capacitance of this partially fi lled capacitor is given by C 5 a 3k 2k 1 1 bC0 (Hint: Treat the system as two capacitors connected in series, one with dielectric in it and the other one empty.)

Two capacitors give an equivalent capacitance of Cp when connected in parallel and an equivalent capacitance of Cs when connected in series. What is the capacitance of each capacitor?

An isolated capacitor of unknown capacitance has been charged to a potential difference of 100 V. When the charged capacitor is disconnected from the battery and then connected in parallel to an uncharged 10.0-mF capacitor, the voltage across the combination is measured to be 30.0 V. Calculate the unknown capacitance.

Two charges of 1.0 mC and _2.0 mC are 0.50 m apart at two vertices of an equilateral triangle as in Figure P16.60. (a) What is the electric potential due to the 1.0-mC charge at the third vertex, point P ? (b) What is the electric potential due to the _2.0-mC charge at P ? (c) Find the total electric potential at P. (d) What is the work required to move a 3.0-mC charge from infi nity to P.

Find the equivalent capacitance of the group of capacitors shown in Figure P16.61.

A spherical capacitor consists of a spherical conducting shell of radius b and charge _Q concentric with a smaller conducting sphere of radius a and charge Q. (a) Find the capacitance of this device. (b) Show that as the radius b of the outer sphere approaches infi nity, the capacitance approaches the value a/ke _ 4pP0a.

The immediate cause of many deaths is ventricular fi brillation, an uncoordinated quivering of the heart, as opposed to proper beating. An electric shock to the chest can cause momentary paralysis of the heart muscle, after which the heart will sometimes start organized beating again. A defi brillator is a device that applies a strong elec- tric shock to the chest over a time of a few milliseconds. The device contains a capacitor of a few microfarads, charged to several thousand volts. Electrodes called paddles, about 8 cm across and coated with conducting paste, are held against the chest on both sides of the heart. Their handles are insulated to prevent injury to the operator, who calls Clear! and pushes a button on one paddle to discharge the capacitor through the patients chest. Assume an energy of 300 W _ s is to be delivered from a 30.0-mF capacitor. To what potential difference must it be charged?

When a certain air-fi lled parallel-plate capacitor is connected across a battery, it acquires a charge of 150 mC on each plate. While the battery connection is maintained, a dielectric slab is inserted into, and fi lls, the region between the plates. This results in the accumulation of an additional charge of 200 mC on each plate. What is the dielectric constant of the slab?

Capacitors C1 _ 6.0 mF and C2 _ 2.0 mF are charged as a parallel combination across a 250-V battery. The capacitors are disconnected from the battery and from each other. They are then connected positive plate to negative plate and negative plate to positive plate. Calculate the resulting charge on each capacitor.

The energy stored in a 52.0-mF capacitor is used to melt a 6.00-mg sample of lead. To what voltage must the capacitor be initially charged, assuming the initial temperature of the lead is 20.0C? Lead has a specifi c heat of 128 J/kg_C, a melting point of 327.3C, and a latent heat of fusion of 24.5 kJ/kg.

Metal sphere A of radius 12.0 cm carries 6.00 mC of charge, and metal sphere B of radius 18.0 cm carries _4.00 mC of charge. If the two spheres are attached by a very long conducting thread, what is the fi nal distribution of charge on the two spheres?

An electron is fi red at a speed v0 _ 5.6 _ 106 m/s and at an angle u0 _ _45 between two parallel conducting plates that are D _ 2.0 mm apart, as in Figure P16.68. If the voltage difference between the plates is _V _ 100 V, determine (a) how close, d, the electron will get to the bottom plate and (b) where the electron will strike the top plate.