Tutorial 4b – Electric Potential
23–1 Electric Potential
1. (I) What potential difference is needed to stop an electron that has an initial velocity
y  5.0 3 105 m/s?
2. (I) How much work does the electric field do in moving a proton from a point with a potential
of 1 185 V to a point where it is 2 55 V? Ans: 3.84 × 1017J
4. (II) The work done by an external force to move a 2 9.10 mC charge from point a to point b
is 7.00 3 102 4 J. If the charge was started from rest and had 2.10 3 102 4 J of kinetic energy
when it reached point b, what must be the potential difference between a and b? Ans: 53.8 V
23–2 Potential Related to Electric Field
6. (I) The electric field between two parallel plates connected to a 45-V battery is 1300 V/m.
How far apart are the plates? Ans: 3.5 × 102 m
8. (I) What is the magnitude of the electric field between two parallel plates 4.0mm apart if the
potential difference between them is 110 V? Ans: 2.8 × 104 V/m
23–3 Potential Due to Point Charges
24. (I) A point charge Q creates an electric potential of 1 185 V at a distance of 15 cm. What is
Q (let V  0 at r  ` 2 ? Ans: 3.1× 109 C
26. (II) Two point charges, 3.4 mC and 2 2.0 mC , are placed 5.0 cm apart on the x axis. At what
points along the x axis is (a) the electric field zero and (b) the potential zero? Let V  0 at
r ` .
Ans: (a) 16 cm left of q2 (b) The two locations where the potential is zero are 1.9 cm from the
negative charge towards the positive charge, and 7.1 cm from the negative charge away from
the positive charge.
28. (II) Point a is 26 cm north of a 2 3.8 mC point charge, and point b is 36 cm west of the charge
(Fig. 23–27). Determine (a) Vb  Va , and (b) Eb  Ea (magnitude and direction).
Ans: (a) 3.6 × 104 V (b) 5.7 × 10 5 V/m, 62o
32. (II) Two equal but opposite charges are separated by a distance d, as shown in Fig. 23–28.
Determine a formula for VBA  VB  VA for points B and A on the line between the charges
situated as shown.
Ans: 2q(2b-d)/4o d(d-b)
23–4 Potential Due to Charge Distribution
34. (II) Three point charges are arranged at the corners of a square of side , as shown in Fig. 23–29.
What is the potential at the fourth corner (point A), taking V  0 at a great distance?
Ans: (2Q/4o 2l)(2 + 1)
42. (I) Draw a conductor in the shape of a football. This conductor carries a net negative charge,
2 Q. Draw in a dozen or so electric field lines and equipotential lines.
44. (II) A metal sphere of radius r0  0.44 m carries a charge Q  0.50 mC. Equipotential
surfaces are to be drawn for 100-V intervals outside the sphere. Determine the radius r of (a)
the first, (b) the tenth, and (c) the 100th equipotential from the surface.
Ans: 0.444 m, 0.49 m, 21 m
23–8 Electrostatic Potential Energy; Electron Volt
55. (I) What potential difference is needed to give a helium nucleus  Q  3.2 3 102 19 C  125 keV
of kinetic energy?
Solution
56. (I) What is the speed of (a) a 1.5-keV (kinetic energy) electron and (b) a 1.5-keV proton?
Ans: (a) 2.3 × 107 m/s (b) 5.4 × 10 5 m/s
58. (II) An alpha particle (which is a helium nucleus, Q  1 2e, m  6.64 3 102 27 kg ) is emitted
in a radioactive decay with kinetic energy 5.53 MeV. What is its speed?
Ans: (a) 1.63 × 107 m/s