Question

ABCD is a square of side 4cm, Charges
+2nC, -2nC and +3nC are placed at corners
A, B and
C respectively. Calculate the work done in
transferring a charge of +4nC from point D
to)
centre of the square.

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Answer 1

ABCD is a square of side 4 cm, charged +2nC, -2nC and +3nC are placed at corners A, B and C respectively.

We have to calculate the work done in transferring a charge of +4nC from point D to the centre of the square.

∵ work done from point D to the centre of square = charge (which needed to transfer from D to O) × potential change from D to O.

I.e., W = Q ∆V

∆V = potential at O due to A, B and C - potential at D due to A, B and C

= $\frac{K(q_A+q_B+q_C)}{\frac{a}{\sqrt{2}}}-\left(\frac{Kq_A}{a}+\frac{Kq_B}{\sqrt{2}a}+\frac{Kq_C}{a}\right)$

= $\frac{9\times10^9(2-2+3)\times10^{-9}}{0.02\sqrt{2}}\frac{9\times10^9\times2\times10^{-9}}{0.04}-\left(\frac{9\times10^9\times2\times10^{-9}}{0.04\sqrt{2}}+\frac{9\times10^9\times3\times10^{-9}}{0.04}\right)$

= 147.792 Volts ≈ 148 volts

now works done = Q∆V

= 4 × 10^-9 × 148

= 5.92 × 10^-7 J

Therefore the work done in transferring the charge 4nC from D to the centre of square is 5.92 × 10^-7 J.