2.12 A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of -2\times 10^{-9}C from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm).

Answers (1)

Given,

The initial distance between two charges 

d_{initial}=3cm

The final distance between two charges

d_{final}=4cm

Hence total work is done 

W=q_2\left ( \frac{kq_1}{d_{final}}-\frac{kq_1}{d_{initial}}\right )=\frac{kq_1q_2}{4\pi\epsilon _0}\left ( \frac{1}{d_{final}}-\frac{1}{d_{initial}} \right )

W=9*10^9*8*10^{-3}*(-2*10^{-9})\left ( \frac{1}{0.04}-\frac{1}{0.03} \right )=1.27J

The path of the charge does not matter, only initial and final position matters.

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