Please Note: It may not always be possible to include the necessary special characters, superscripts, subscripts, etc. in e-mail responses to this group of exercises. We suggest that you discuss this matter with your professor/class and decide upon a system for indicating such characters. You may cut/paste some characters and/or Greek letters from Microsoft Word, using the Insert menu. Alternatively, we suggest that you agree upon abbreviations for or spell out symbols, Greek letters, or characters and indicate superscripts and subscripts by using "sup", "sub", or up/down carats.

1			A positive charge is initially at rest in an electric field and is free to move. Does the charge start to move toward a position of higher or lower potential? What happens to a negative charge in the same situation?
2			If the potential increases as you move from point P in the +x-direction, but the potential does not change as you move from P in the y- or z-directions, what is the direction of the electric field at P?
3			A hydrogen atom has a single proton at its center and a single electron at a distance of approximately 0.0529 nm from the proton. (a) What is the electric potential energy in joules? (b) What is the significance of the sign of the answer?
4			A charge of +2.0 mC is located at x = 0, y = 0 and a charge of -4.0 mC is located at x = 0, y = 3.0 m. What is the electric potential due to these charges at a point with coordinates x = 4.0 m, y = 0?
5			Charges of +2.0 nC and -1.0 nC are located at opposite corners, A and C, respectively, of a square which is 1.0 m on a side (Fig. 17.51). What is the electric potential at a third corner, B, of the square (where there is no charge)? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Fig. 17.51::/sites/dl/free/0070524076/58000/17_051.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Fig. 17.51 (4.0K)</a>Fig. 17.51
6			(a) Find the potential at points a and b in Fig. 17.53 for charges Q1 = +2.50 nC and Q2 = -2.50 nC. (b) How much work must be done by an external agent to bring a point charge q from infinity to point b? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Fig. 17.53::/sites/dl/free/0070524076/58000/17_053.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Fig. 17.53 (5.0K)</a>Fig. 17.53
7			In a region where there is an electric field, the electric forces do +8.0 × 10-19 J of work on an electron as it moves from point X to point Y. (a) Which point, X or Y, is at a higher potential? (b) What is the potential difference, VY - VX, between point Y and point X?
8			It is believed that a large electric fish known as Torpedo occidentalis uses electricity to shock its victims. A typical fish can deliver a potential difference of 0.20 kV for a duration of 1.5 ms. This pulse delivers charge at a rate of 18 C/s. (a) What is the rate at which this work is done by the electric organs during a pulse? (b) What is the total amount of work done during one pulse?
9			Point P is at a potential of 500.0 kV and point S is at a potential of 200.0 kV. The space between these points is evacuated. When a charge of +2e moves from P to S, by how much does its kinetic energy change?
10			A helium nucleus (charge +2e) moves through a potential difference ΔV = -0.50 kV. Its initial kinetic energy is 1.20 × 10-16 J. What is its final kinetic energy?
11			A parallel plate capacitor has a capacitance of 2.0 μF and plate separation of 1.0 mm. (a) How much potential difference can be placed across the capacitor before dielectric breakdown of air occurs (Emax = 3 × 106 V/m)? (b) What is the magnitude of the greatest charge the capacitor can store before breakdown?
12			A parallel plate capacitor has a capacitance of 1.20 nF. There is a charge of magnitude 0.800 μC on each plate. (a) What is the potential difference between the plates? (b) If the plate separation is doubled, while the charge is kept constant, what will happen to the potential difference?
13			A parallel plate capacitor has a charge of 0.020 μC on each plate with a potential difference of 240 V. The parallel plates are separated by 0.40 mm of air. What energy is stored in this capacitor?
14			A defibrillator is used to restart a person's heart after it stops beating. Energy is delivered to the heart by discharging a capacitor through the body tissues near the heart. If the capacitance of the defibrillator is 9 μF and the energy delivered is to be 300 J, to what potential difference must the capacitor be charged?
15			A thundercloud is at a potential of -1.00 × 108 V with respect to Earth's surface. If a charge of 25.0 C is transferred to the Earth during a lightning strike, completely discharging the cloud, find the energy delivered to Earth.
16			Charges of -12.0 nC and -22.0 nC are separated by 0.700 m. What is the potential midway between the two charges?
17			If an electron moves from one point at a potential of -100.0 V to another point at a potential of +100.0 V, how much work is done by the electric field?
18			The potential difference across a cell membrane is -90 mV. If the membrane's thickness is 10 nm, what is the magnitude of the electric field in the membrane? Assume the field is uniform.
19			An axon has the outer part of its membrane positively charged and the inner part negatively charged. The membrane has a thickness of 4.4 nm and a dielectric constant κ = 5. If we model the axon as a parallel plate capacitor whose area is 5 μm2, what is its capacitance?