Three point charges q_1, q_2, and q_3 are situated at three corners of a rectang

Question

Three point charges q_1, q_2, and q_3 are situated at three corners of a rectangle as shown in the diagram below. Here q_1 = +5.00 mu C, q_2 = -5.00 mu C, q_3 = +7.00 mu C. (a) What is the electric potential at the free corner where there is no charge? 1.9e6 What is the electric potential due to a point charge at a particular distance from it? Did you consider the sign of each charge when calculating the electric potential? V (b) What charge should be placed at the free corner for the electric potential at the center of the rectangle to be zero? Include both magnitude and sign if applicable. mu C

Explanation / Answer

(a) The principle of superposition applies to the electric potential (as it does to the electrostatic force and the electric field), so the potential at P is the sum of the potentials due to all of the charges present.

V = ke [q1/r1 +q2/r2 +q3/r3]

The values of the charges should have been q1 = +5.00 nC, q2 = -5.00 nC and q3 = +7.00 nC.
V = 9.00 * 10^9[5.00/ 5.00 + (-5.00/4.00) +7.00/3.00] * 10^-9
= 18.75 V

b)

To make the electric potential at center zero, charge on the free corner will be

Vc = 0

Vc = V1 + V2 + V3 + V4 = 0

Vc = k*Q1/r1 + k*Q2/r2 + k*Q3/r3 + k*Q4/r4 = 0

Now every charge is at the same distance from center

r1 = r2 = r3 = r4 = 0

So

Total sum of charge should be zero

Q = Q1 + Q2 + Q3 + Q4 = 0

Q4 = - 7.00 uC

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