Question

Three point charges + Q + 2Q and q are placed at the vertices of an equilateral triangle. The value of charge q in terms of Q so that electrical potential energy of the system is zero, is given by ______.

Options

• q = \[\frac {1}{3}\]Q

• q = \[\frac {2}{3}\]Q

• q = -\[\frac {2}{3}\]Q

• q = -\[\frac {3}{2}\]Q

Answer 1

Three point charges + Q + 2Q and q are placed at the vertices of an equilateral triangle. The value of charge q in terms of Q so that electrical potential energy of the system is zero, is given by q = -\[\frac {2}{3}\]Q.

Explanation:

Potential energy due to +q and +2q,

U₁ = \[\frac {Kq(2q)}{r}\]

\[\therefore\] Potential energy due to +q and +Q,

U₂ = \[\frac {KqQ}{r}\]

\[\therefore\] Potential energy due to +Q and +2q,

U₃ = \[\frac {KQ(2q)}{r}\]

Given Potential energy of systems = 0

\[\therefore\] U₁ + U₂ + U₃ = 0

\[\frac{\mathrm{Kq}(2\mathrm{q})}{\mathrm{r}}+\frac{\mathrm{KqQ}}{\mathrm{r}}+\frac{\mathrm{KQ}(2\mathrm{q})}{\mathrm{r}}\] = 0

2q + Q + 2Q = 0

3Q = -2q

Q = \[\frac {-2}{3}\]q