Question

At the corners of an equilateral triangle of side a ( $1$ meter), three point charges are placed (each of $0.1C$ ). If this system is supplied energy at the rate of $1kw$, then calculate the time required to move one of the mid-point of the line joining the other two.

• A. 50 h
• B. 60 h
• C. 48 h
• D. 54 h

Answer 1

Answer: (A)

Initial potential energy of the system
$=\frac{1}{4\pi {ϵ}_0}\left[\frac{q^2}{a}+\frac{q^2}{a}+\frac{q^2}{a}\right]$
$=\frac{1}{4\pi {ϵ}_0}\left(\frac{3q^3}{a}\right)$
$=9\times 10^9\left(3\times \frac{(0.1{)}^2}{1}\right)$
$=27\times 10^{7}J$
Let charge at $A$ is moved to mid-point $O$,
Then final potential energy of the system
$U_f=\frac{1}{4\pi {ϵ}_0}\left(\frac{q^2}{a^2}\right)$
$=45\times 10^{7}J$
Work done $=U_f-U_i=18\times 10^{7}J$
Also, energy supplied per sec $=1000J$ (given)
Time required to move one of the mid-point of the line joining the other two
$t=\frac{18\times 10^7}{1000}=18\times 10^{4}s=50h$