(a) Two point charges +Q_{1}  and-Q_{2} are placed r distance apart. Obtain the expression for the amount of work done to place a third chargeQ_{3} at the midpoint of the line joining the two charges.

(b) At what distance from charge +Q_{1} on the line joining the two charges (in terms of Q_{1},Q_{2} and r) will this work done be zero.

 

 
 
 
 
 

Answers (1)
S safeer

a)

\\W_{Q_1q_3}=\frac{kQ_1q_3}{r/2}=2\frac{kQ_1q_3}{r}\\\\W_{Q_2q_3}=-\frac{kQ_1q_3}{r/2}=-2\frac{kQ_1q_3}{r}\\\\Total \ work=2\frac{kQ_1q_3}{r}-2\frac{kQ_1q_3}{r}=\frac{q_3(Q_1-Q_2)}{2\pi\epsilon_0r}

b)

Let x be the required distance

\\\frac{kQ_1}{x}-\frac{kQ_2}{x-r}=0\\\\x=\frac{Q_1r}{Q_1-Q_2}

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