Question

Plz help with this question
ABCD is a square of side 4cm. If +2nC,-2nC and +3nC is placed atABC then calculate the workdone in moving a charge +4nC from D to the centre of the square.
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Answer 1

Given ABCD is a square of side 4cm. If +2nC,-2nC and +3nC is placed atABC then calculate the work done in moving a charge +4nC from D to the centre of the square.

They have given side 4 cm = 0.04 m , qₐ = - 2 x 10⁻⁹, qb = 3 x 10⁻⁹ qc = 3 x 10⁻⁹

Potential due to three charges at A, B and C:

So Vd = Va + Vb + Vc = K[qb + √2(qa + qc)] / √2 r

                        Vd = 9 x 10⁹[ 3 x 10⁻⁹ + √2(-2 x  10⁻⁹ + 3 x  10⁻⁹)] / √2 x 0.04

                       Vd = 9 x  10⁹ ( 10⁻⁹(3 + √2) / √2 x 0.04

                      Vd = 39.7279 / 0.05656

                       Vd = 702.2970 V

Now work done W = q v

                              = 4 x  10⁻⁹ x 702.2970

                       W = 2809.1 x  10⁻⁹

                       W = 2.8 μ J