Question

A charge of $10$ $\mu C$ is brought from infinity to point $P$ in an external electric field. Point $P$ is located at a distance of $5$ cm away from $5$ $\mu C$ charge. Calculate the work done to bring the $10$ $\mu C$ to point $P$ from infinity?

• (A) $90$ J
• (B) $9$ J
• (C) $900$ J
• (D) $9000$ J

Answer 1

The Correct Option is B

Explanation:
The electrostatic potential is given by:$V=\frac{W}{q}$The electrostatic potential due to a point charge is given by:$V=\frac{Kq}{r}[\because K=\frac{1}{4\pi {ϵ}_0}]$Where $W=$ Work, $q=$ charge and $r=$ distanceGiven: $q_1=5\mu C$ $r=5$ cm $=5\times {10}^{-2}$ m $q_2=10\mu C$The electric potential due to $5\mu C$ at a distance of $5$ cm away from it is$V=\frac{9\times {10}^9\times 5\times {10}^{-6}}{5\times {10}^{-2}}=9\times {10}^{5}V$The work done in moving the charge of $10\mu C$ from infinity to $P$ is:$W=V\times q$$=9\times {10}^5\times 10\times {10}^{-6}$$=9$ JHence, the correct option is (B).