The highest magnetic fields in the world are generated whenINT large arrays, or "

By moving a I 0 nC charge from point A to point B, you determine that the electric potential at Bis 150 V. What would be the potential at B if a 20 nC charge were moved from A to B?

Charge q is fired through a small hole in the positive plate of a capacitor, as shown in Figure Q2 l .2. a. If q is a positive charge, does it speed up or slow down inside the capacitor? Answer this question twice: (i) Using the con- FIGURE 0212 cept of force. (ii} Using the concept of energy.b. Repeat part a if q is a negative charge

Why is the potential energy of two opposite charges a negative number? (Note: Saying that the formula gives a negative number is not an explanation.}

An electron (q = - e} completes half of a circular orbit of radius r around a nucleus with Q = +3e, as shown in Figure Q2 l .4.

An electron moves along the trajectory from i to f in Figure Q2 l .5. a. Does the electric potential energy increase, decrease, or stay the same? Explain. b. Is the electron's speed at f greater than, less than, or 5equal to its speed at i? Explain.

The graph in Figure Q21.6 shows the electric potenti al along the x-axis. Draw a graph of the potential energy of a 0.10 C charged particle in this region of space, providing a numerical scale on the energy axis.

As shown in Figure Q2 l.7, two protons are launched with the same speed from point 1 inside a parallel-plate capacitor. One proton moves along the path from 1 to 2, the other from 1 to 3. Points 2 and 3 are the same distance from the positive plate. a. ls 6.U1- z, the change in potential energy along the path I ~ 2, larger than, smaller than, or equal to fl U1 _ 3? Explain.b. Is the proton's speed v2 at point 2 larger than, smaller than, or equal to the proton's speed v3 at point 3? Explain.

Each part of Figure Q2 1.8 shows one or more point charges. The charges have equal magnitudes. If a positive charge is moved from posi tion i to posi tion f, does the electric potential energy increase, decrease, or stay the same? Explain.

Figure Q21 .9 shows two points inside a capacitor. Let V = 0 V at the negative plate. a. What is the ratio Vz/Vi of the electric potential at these two points? Explain. b. What is the ratio 2/1 of the e lectric field strength at these two points? Explain.

capacitor with plates separated by distance d is charged to a potential difference 6.Vc. All wires and batteries are disconnected, then the two plates are pulled apart (with insulated handles) to a new separation of distance 2d. a. Does the capacitor charge Q change as the separation increases? If so, by what factor? If not, why not? b. Does the electric field strength E change as the separation increases? If so, by what factor? If not, why not? c. Does the potential difference 6.Vc change as the separation increases? If so, by what factor? If not, why not?

Rank in order, from most positive to most negative, the electric potentials Vi to V5 at points I to 5 in Figure Q21. I I. Explain.

Figure Q21. l 2 shows two points near a positive point charge. a. What is the ratio Vi/V2 of the electric potentials at these two points? Explain. b. What is the ratio 1/2 of the electric field strengths at these two points? Explain.

Each part of Figure Q2 l. l 3 shows three points in the vicinity of two point charges. The charges have equal magnitudes. Rank in order, fron:iJargest to smallest, the potentials V1, V2, and V3.

a. Suppose that E = i5 throughout some region of space. Can you conclude that V = 0 V in this region? Explain. b. Suppose that V = 0 V throughout some region of space. Can you conclude that E = i5 in this region? Explain.

Rank in order, from largest to smallest, the electric field strengths 1, 2, 3, and 4 at the four labeled points in Figure Q21. 15. Explain.

Figure Q21.16 shows an electJic field diagram. Rank in order, from highest to lowest, the electJic potentials at points a, b, and c.

Figure Q21. l 7 shows a negatively charged electroscope. The gold leaf stands away from the rigid metal post. Is the electric potential of the leaf higher than, lower than, or equal to the potential of the post? Explain.

Rank in order, from largest to smallest, the energies ( Uc)1 to (Uc)4 stored in each of the capacitors in Figure Q2 l. l 8. Explain.

A parallel-plate capacitor with plate separation d is connected to a battery that has potential difference b.Vbat Without breaking any of the connections, insulating handles are used to increase the plate separation to 2d. a. Does the potential difference b.Vc change as the separation increases? If so, by what factor? If not, why not? b. Does the capacitance change? If so, by what factor? If not, why not? c. Does the capacitor charge Q change? If so, by what factor? If not, why not?

proton is launched from point in Figure Q21.20 with an initial 2 ' velocity of 3.9 X 1 o-5 mis. By how much has its kinetic energy changed, in eV, by the time it passes through point 2?

A 1.0 nC positive point charge is located at point A in Figure Q21.2 l. The electric potential at point B is A.9.0V B. 9.0sin 30 V C. 9.0cos 30 V D. 9.0tan30 V

A I 00 V battery is connected across the plates of a parnllel-plate capacitor. lf a sheet of Teflon is slid between the plates, without disconnecting the battery, the elecllic field between the plates A. Increases. B. Decreases.C. Remains the same.

The electric potential is 300 V at x = 0 cm, is - I 00 V at x = 5 cm, and varies linearly with x. rr a positive charge is released from rest at x = 2.5 cm, and is subject only to electric forces, the charge wi II A. Move to the right. B. Move to the left. C. Stay at x = 2.5 cm. D. Not enough information to tell.

What is the potential at point c? B. - 350 V C. - lOOV E. 400 V

At which point, a, b, ore, is the magnitude of the electric field the greatest?

What is the approximate magnitude of the electric field at point c? A. IOO V/m B. 300 Y/m C. 800 V/m D. 1500 V/m E. 3000 V/m

The direction of the elect ric field at point bis closest to which direction? A. Right B. Up C. Left D. Down

A + JO nC charge is moved from point c to point a. How much work is required in order to do this? A. 3.5 x I0-6 J B. 4.0 x I0-6 J C. 3.5 x I0-3 J D. 4.0 x 10-3 J E. 3.5 J

A bug zapper consists of two metal plates connected to a high-voltage power supply. The voltage between the plates is set to give an electric field s lightly less than 1 X I 06 V /m. When a bug flies between the two plates, it increases the field enough to initiate a spark that incinerates the bug. lf a bug zapper has a 4000 Y power supply, what is the approximate separation between the plates? A. 0.05 cm B. 0.5 cm C. 5 cm D. 50 cm

An atom of helium and one of argon are singly ionized-one electron is removed from each. The two ions are then accelerated from rest by the electric fi eld between two plates with a potential difference of 1 SOY. After accelerating from one plate to the other, A. The helium ion has more kinetic energy. B. The argon ion has more kinetic energy. C. Both ions have the same kinetic energy. D. There is not enough information to say which ion has more kinetic energy.

The dipole moment of the heart is shown BIO at a particular instant in Figure Q2 l .3 l. Which of the following potential differences will have the largest positive value? A. Vi - V2 B. Vi - V3 C.V2 - V1 D. V3 - V

Two electrodes connected to a 9.0 V banery a re charged to 45 nC. What is the capacitance of the electrodes?

Initially. the switch in Figure P2 I .33 is open and the capacitor is unc harged. How much charge flows through the switch after the switch is closed?

A 1.2 nF parallel-plate capacitor has an air gap between its plates. Its capacitance increases by 3.0 nF when the gap is filled by a die lectric. What is the dielectric constant or that dielectric?

A science-fair radio uses a homemade capacitor made of two 35 cm X 35 cm sheets of aluminum foil separated by a 0.25-mm-thick sheet of paper. What is its capacitance?

A 25 pF parallel-plate capacitor with an a ir gap between the plates is connected to a 100 V battery. A Te flon slab is then inserted between the plates and completely fills the gap. What is the change in the charge on the positive plate when the Te flon is inserted?

Two 2.0-cm-diameter electrodes with a 0. 10-mm-thick sheet of Te flon between them are auached to a 9.0 V battery. Without disconnecting the bauery, the Teflon is removed. What are the c harge, potenti al difference, and electric fie ld (a) before a nd (b) after the Tefl on is removed?

A parallel-plate capacitor is connected to a battery and s tores 4.4 nC of charge. Then, while the battery remains connected, a sheet of Te flon is inserted between the plates. a. Does the capacitor's charge increase or decrease? b. By how much does the charge change?

A parallel-plate capac itor is charged by a 12.0 V banery, then the battery is removed. a. What is the potential difference between the plates after the battery is disconnected? b. What is the potential difference between the plates after a sheet of Teflon is inserted between them?

To what potential should you charge a 1.0 F capac itor to s tore 1.0 J of energy?

A pair of I 0 F capacitors in a high-power laser are charged to 1.7 kV. a. What charge is stored in each capaci tor? b. How much energy is stored in each capacitor?

Capacitor 2 has half the capacitance and twice the potential difference as capacitor I. What is the ratio (Uc) 1/(Uc h ?

Two uncharged metal spheres, spaced 15.0 cm apa11, have a capacitance of 24.0 pF. How much work would it take to move 12.0 nC of charge from one sphere to the other?

50 pJ of energy is stored in a 2.0 cm X 2.0 cm x 2.0 cm region of uniform electric field. What is the e lectric field strength?

A 2.0-cm-diameter parallel-plate capacitor with a spacing of 0.50 mm is charged to 200 V. What are (a) the total energy stored in the electric field and (b) the energy density?

What is the change in electric potential energy of a 3.0 nC point charge when it is moved from point A to point B in Figure P2 I .46?

What is the potential difference 6.V34 in Figure P2 I .47?

A - 50 nC charged particle is in a uniform electric field INr E = ( I 0 V /m, east) . An e xternal force moves the particle 1.0 m no11h, then 5.0 m east, then 2.0 m south, and finally 3.0 m west. The particle begins and ends its mot ion with zero velocity. a. How much work is done on it by the external force? b. What is the potential difference between the particle's fina l and initial positions?

Al a d is tance r from a point charge, the electric potential is INT 3000 Y and the magnitude of the e lectric fie ld is 2.0 X I 05 V /m. a. What is the distance r? b. Whal are the electric potential and the magnitude of the electric field at distance r/2 from the charge?

The 4000 V equipotential surface is I 0.0 cm farther from a positi vely charged particle than the 5000 V equipotential surface. What is the charge on the particle?

What is the electric potential energy of the electron in Figure P2 I .5 I? The protons are fixed and can't move.

Two point charges 2.0 cm apart have an electric potential energy - 180 J. The total charge is 30 nC. What are the two charges?

Two pos itive point charges are 5.0 cm apart. If the e lectric INT potential energy is 72 J, what is the magnitude of the force between the two charges?

3.0 nC charge is at x = 0 cm and a - 1.0 nC charge is at x = 4 cm. At what point or points on the x-axis is the e lectric potential zero?

A - 3.0 nC charge is on the x-axis at x = - 9 cm and a +4.0 nC charge is on the x-axis at x = 16 cm. At what point or points on the y-axis is the electric potential zero?

A -2.0 nC charge and a + 2.0 nC charge are located on the INT x-axis at x = -1.0 cm and x = + 1.0 cm, respectively. a. At what position or positions on the x-axis is the electric field zero? b. At what position or positions on the x-axis is the electric potentia 1 zero? c. Draw graphs of the electric field strength and the electric potential along the x-axis

A - LO.O nC point charge and a + 20.0 nC point charge are INT 15.0 cm apart on the x-axis. a. What is the electric potential at the point on the x-axis where the electric field is zero? b. What are the magnirude and direction of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

A 2.0-mm-diameter glass bead is positively charged. The potential difference between a point 2.0 mm from the bead and a point 4.0 mm from the bead is 500 V. What is the charge on the bead?

In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm. a. What is the electric potential of the proton at the position of the electron? b. What is the electron's potential energy?

What is the electric potential at the point indicated with the dot in Figure P2 I .60?

a. What is the e lectric potential at point A in Figure P2 I .6 I? b. What is the potential energy of a proton at point A?

A proton's speed as it passes point A is 50,000 m/s. It fol lows the trajectory shown in Figure P2 I .62. What is the proton's speed at point B?

A proton follows the path shown in Figure P21.63. Its initial speed is v0 = l.9 X 106 111/s. What is the proton's speed as it passes through point P?

Electric outlets have a voltage of approximately 120 V between the two parallel slots. Estimate the electric field strength between these two slots.

Estimate the magnitude of the electric field in a cell mem brane with a thickness of 8 nm.

A Na+ ion moves from inside a cell, where the e lectric poten tial is - 70 mV, to outside the cell, where the potential is 0 Y. What is the change in the ion's electric potential energy as it moves from inside to outside the cell? Does its energy increase or decrease?

Suppose that a molecular ion with charge - I Oe is embedded within the 5.0-nm-thick ce ll membrane of a cell with membrane potential -70 mY. What is the electric force on the molecule?

The electric field strength is 50,000 V/m inside a parallelplate capacitor with a 2 .0 mm spacing. A proton is released from rest at the positive plate. What is the proton's speed when it reaches the negative plate?

A parallel-plate capacitor is charged to 5000 Y. A proton is fired intothecenterofthecapacitor at a speed of 3.0 X I 05 m/s, as shown in Figure P21.69. The proton is deflected while inside the capacitor, and the plates are long enough that the proton will hit one of them before emerging from the far side of the capacitor. What is the impact speed of the proton?

A proton is released from rest at the positive plate of a parallel- plate capacitor. It crosses the capacitor and reac hes the negative plate with a speed of 50,000 mis. What will be the proton's final speed jf the experiment is repeated with double the amount of charge on each capacitor plate?

The electric field strength is 20,000 V/m inside a parallel plate capacitor with a I .Omm spacjng. An e lectron is released from rest at the negative plate. What is the electron's speed when it reaches the positive plate?

In the early 1900s, Robert Millikan used small charged drop INT lets ofoil , suspended in an electric field, to makethe first quantitative measurements of the electron 's charge. A 0. 70-11m-diameter droplet of oil, having a charge of +e, is suspended in midair between two horizontal plates of a parallel-plate capacitor. The upward electric force on the droplet is exactly balanced by the downward force of gravity. The oil has a density of 860 kglm3, and the capacitor plates are 5.0 mm apart. What must the potential difference between the plates be to hold the droplet in equil ibrium?

Two 2.0-cm-diameter di sks spaced 2.0 mm apart form a parallel-plate capaci tor. The electric field between the disks is 5.0 X 105 Y/m. a. What is the voltage across the capacitor? b. How much charge is on each disk? c. An e lectron is launched from the negative plate. It strikes the positive plate at a speed of 2.0 X I 07 m/s. What was the electron's speed as it left the negative plate?

In proton-beam therapy, a high-energy beam of protons is fired at a tumor. The protons come to rest in the tumor, depositing their kinetic energy and breaking apart the tumor's DNA, thus killing its cells. For one patient, it is desired that 0. 10 J of proton energy be deposited in a tumor. To create the proton beam, the protons are accelerated from rest through a I 0 MY potential di fference. What is the total charge of the protons that must be fired at the tumor to deposit the required energy?

A 2.5-mm-diameter sphere is charged to - 4.5 nC. An electron fired directly at the sphere from far away comes to within 0.30 mm of the surface of the target before being reflected. a. What was the electron's initial speed? b. At what distance from the surface of the sphere is the electron's speed half of its initial value? c. What is the acceleration of the electron at its turning point?

A proton is fired from far away toward the nucleus of an iron atom. Jron is element number 26, and the diameter of the nucleus is 9.0 fm. ( L [m = I 0-15 m.) What initial speed does the proton need to just reach the su1face of the nucleus? Assume the nucleus remains at rest.

Two 10.0-cm-diameter electrodes 0.50 cm apart form a parallel- plate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. After a long time, the capacitor is disconnected from the battery but is not discharged. What are the charge on each electrode, the electric field strength inside the capacitor, and the potential difference between the electrodes a. Right after the battery is disconnected? b. After insulating handles are used to pull the electrodes away from each other until they are 1.0 cm apa1t?

Two 10.0-cm-diameter electrodes 0.50 cm apart form a parallel- plate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. What are the charge on each electrode, the electric field strength inside the capacitor, and the potential difference between the electrodes a. While the capacitor is attached to the battery? b. After insulating handles are used to pull the electrodes away from each other until they are 1.0 cm apart? The electrodes remain connected to the battery during this process.

Determine the magnitude and direction of the electric field at points I and 2 in Figure P2 I .79.

Figure P2 I .80 shows a series of equipotential curves. a. Is the electric field strength at point A larger than, smaller than, or equal to the field strength at point B? Explain. b. ls the electric field strength at point C larger than, smaller than, or equal to the field strength at point D? Explain. c. Determine the electric field E at point D. Express your answer as a magnitude and direction.

Figure P2 l.8 I shows theelecnic potential on a grid whose squares are 5.0 cm on a side. a. Reproduce this figure on c. your paper, then draw the A 50 V, 75 V, and 100 V equi- potential surfaces. b. Estimate the electric field (strength and direction) at points A, B, C, and D. c. Draw the electric field vec- Po1en1ial in v tors al points A, 8, C, and D FIGURE P21 .81

capacitor consists of two 6.0-cm-diameter circular plates INT separated by 1.0 mm. The plates are charged to 150 V, then the battery is removed. a. How much energy is stored in the capacitor? b. How much work must be done to pull the plates apart to where the distance between them is 2.0 mm?

The dielectric in a capaci tor serves two purposes. It increases the capacitance, compared to an otherwise identical capacitor with an air gap, and it increases the maximum potential difference the capacitor can support. Tf the electric field in a material is s ufficiently strong, the material wi ll suddenly become able to conduct, creating a spark. The critical field strength, at which breakdown occurs, is 3.0 MY /m for air, but 60 MV/m for Teflon. a. A parallel-plate capacitor consists of two square plates, 15 cm on a side, spaced 0.50 mn) apart with only air between them. What is the maximum energy that can be stored by the capacitor? b. What is the maximum energy that can be stored if the plates are separated by a 0.50-mm-thick Teflon sheet?

The highest magnetic fields in the world are generated when INT large arrays, or " banks," of capacitors are discharged through the copper coils of an electromagnet. At the National High Magnetic Field Laboratory, the total capacitance of the capacitor bank is 32 mF. These capacitors can be charged to 16 kV. a. What is the energy stored in the capacitor bank when it is fully charged? b. When discharged, the entire energy from this bank flows through the magnet coil in I 0 ms. What is the average power delivered to the coils during this time?

The flash unit in a camera uses a special circuit to "step up" the 3.0 V from the batteries to 300 V, which charges a capacitor. The capacitor is then discharged through a flash lamp. The discharge takes I 0 .s, and the average power dissipated in the flash lamp is I 05 W. What is the capacitance of the capacitor?