Question

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Charges -2q and +3q are fixed at two corners of a square formed with points A and B as shown in the figure. Which statement is true about the electric potential (V) of this arrangement? A. V is the same at points A and B. B. V is zero at point B. C. V is greater at point A than at point B. D. Any path taken from point A to point B has the same change in V.

Answer 1

r = length of diagonal = sqrt(a² + b²)

Electric potential at A is given as

V_A = k (-2q)/b + k(3q)/r = - 2kq/b + 3kq/sqrt(a² + b²)

lets assume a = 1 , b = 2

V_A =  - 2kq/2 + 3kq/sqrt(1² + 2²) = 0.34 kq

V_A = - 2kq/2 + 3kq/sqrt(1² + 2²) = 0.34 q

electric potential at B is given as

V_B = k (-2q)/r + k(3q)/b = - 2kq/sqrt(a² + b²) + 3kq/b

lets assume a = 1 , b = 2

V_B =  - 2kq/sqrt(a² + b²) + 3kq/b

V_B =  - 2kq/sqrt(1² + 2²) + 3kq/2 = 0.61 kq

clearly V_B > V_A

hence statement C is false

D . True

electric potential change a scalar quantity and does not depend on the path taken. it only depends on the initial and final position. hence any path taken between A to B will give same potential change.