Concept #1: Electric Potential

Example #1: Movement of Charges in Potential Fields

Example #2: Potential due to Point Charges

Practice: How far from a 5uC charge will the potential be 100 V?

Practice: A -1uC and a 5uC charge lie on a line, separated by 5cm. What is the electric potential halfway between the two charges?

Example #3: Potential Difference Between Two Charges

Three charges of magnitude |q| = 3.0 x 10-9C are placed along the circumference of a circle with radius R = 1.0m. A charge +q lies at x = -R, a charge -q at y = -R, and a charge -q at x = R.
a. Determine the electric potential at the origin of the circle.
b. If a negative charge with q = -1.5 x 10-9 C brought from r= ∞ and placed at the origin, what is the change in potential energy of the system of charges?

Two particles, with charges of 20.0 nC and -20.0 nC, are located at the points with coordinates (0, 4.00 cm) and (0, -4.00 cm), as shown in the figure below. A third particle with charge 40.0 nC is located at the point (5.00 cm, 0).
Determine the electrical potential at the origin (0,0) due to the three fixed charges (40.0 nC, 20.0 nC, and -20.0 nC).

Two particles, with charges of 20.0 nC and –20.0 nC, are located at the points with coordinates (0, 4.00 cm) and (0, – 4.00 cm), as shown in the figure below. A third particle with charge 10.0 nC is located at the origin (0,0). Determine the electric potential at the point (3.00 cm, 0) due to the three fixed charges (10.0 nC, 20.0 nC, and –20.0 nC).

A 4.0-μC charge is situated at the origin of an xy-coordinate system. What is the potential difference between a point x = 4.0 m and y = -4.0 m because of this charge?
A) -18×103 V
B) 18×103 V
C) 0 V
D) 36×103 V

Which statement below, describing an electrostatic situation of a conductor, is NOT correct?
A) The electric field within a conductor is zero.
B) The electric potential within a conductor is equal everywhere.
C) The electric field outside of a conductor is always perpendicular to the surface.
D) Excess charges of a conductor only reside below the surface, not on the surface.

Consider a square with sides L = 48cm and two negative charges Q = - 2.5 μC placed on the corners labeled with Q in the figure. What is the electric potential in the corner of the square labeled by B?

Two charged spherical conductors are connected by a long conducting wire. A total charge of q > 0 is placed on this combination of two spheres. Sphere 1 has a radius of r1 and sphere 2 has a radius of r2, where r2 > r1. If q1 represents the charge on sphere 1 and q 2 the charge on sphere 2, what is the ratio q1 / q2 of the charges?
1. q1 / q2 = r2 / r1
2. q1 / q2 = r1 / r1 + r2
3. q1 / q2 = (r2 / r1)2
4. q1 / q2 = r2 / r1 + r2
5. None of these
6. q1 / q2 = 1
7. q1 / q2 = (r1 / r2)2
8. q1 / q2 = r1 / r2

Three point charges are held on the circumference of a circle of radius 20 cm as shown in the figure. Assume that the electric potential is defined to be zero at infinity. Determine the electric potential at the center of the circle.
(a) +6.0 x 104 V
(b) +2.3 x 105 V
(c) -4.6 x 105 V
(d) –7.8 x 105 V
(e) zero volts

Let: V = 0 at infinity. Three charges are arranged in the (x, y) plane (as shown in the figure below, where the scale is in meters). Find the electric potential Vo at the origin [coordinates (0 m, 0 m)].

A sphere with radius 2.0 mm carries a 2.0 μC charge. What is the potential difference, VB - VA, between point B 4.0 m from the center of the sphere and point A 6.0 m from the center of the sphere? (The value of k is 9.0x109 N•m2/C2.)A) 1500 VB) -0.63 VC) -1500 VD) 170 V