Point charges q1=+2.00C and q2=2.00C are placed at adjacent corners of a square

Question

Point charges q1=+2.00C and q2=2.00C are placed at adjacent corners of a square for which the length of each side is 2.00 cm . Point a is at the center of the square, and point b is at the empty corner closest to q2. Take the electric potential to be zero at a distance far from both charges.

A) What is the electric potential at point a due to q1 and q2?

b)What is the electric potential at point b?

c)A point charge q3 = -3.00 C moves from point a to point b. How much work is done on q3 by the electric forces exerted by q1 and q2?

Explanation / Answer

A) Electrical potential due to a point charge at a distance d = kq / d

distance of corner to the centre d = sqrt(1^2 + 1^2) = 1.414 cm = 0.01414 m

V = kq1/d + kq2/d

and q1 = -q2

so V = 0

b) distance of b from q2 = 2 cm = 0.02 m

distance of b from q1 = sqrt(2^2 + 2^2) = 2.83 cm = 0.0283 m

V = [ (9 x 10^9 x 2 x 10^-6 ) / 0.0283 ]   + [ (9x 10^9 x -2 x 10^-6) / 0.02 ]

V = - 263957.60 volt

c) Work done = change in PE = qV

W = -3 x 10^-6 x -263957.60 = 0.79 J

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