Question

At the corners of an equilateral triangle of side a $\left(1metre\right)$, 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. $50h$
• B. $60h$
• C. $48h$
• D. $54h$

Answer 1

The correct option is A $50h$

Initial potential energy of the system
$=\frac{1}{4\pi {ϵ}_0}[\frac{q^2}{a}+\frac{q^2}{a}+\frac{q^2}{a}]=\frac{1}{4\pi {ϵ}_0}\left(\frac{3q^2}{a}\right)$
$=9\times {10}^9(3\times \frac{(0.1{)}^2}{1})=27\times {10}^{7}J$
Let charge at $A$ is moved to mid-point $O$, Then final potential energy of the system
$U_f=\frac{1}{4\pi {ϵ}_0}[\frac{2q^2}{\left(a/2\right)}+\frac{q^2}{a}]$
$=5\times \frac{1}{4\pi {ϵ}_0}\left(\frac{q^2}{a^2}\right)=45\times {10}^{7}J$
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
$t=\frac{18\times {10}^7}{1000}=18\times {10}^{4}s=50h$.