Question

Two fixed point charges 4q and -2q are kept 1m apart .where should the third point charge p be kept so that it is in equilibrium

Answer 1

Given : Two fixed point charges 4q and -2q are kept 1 m apart.

To find : The location of third charge p so that it is in equilibrium.

solution : 4q ..................... -2q --------p

a third charge p is placed right side of -2q so that it is in equilibrium as shown above.

let distance of p from -2q is x.

at equilibrium,

force exerted by 4q on p = force exerted by -2q on p

⇒K(4q)(p)/(1 + x)² = k(2q)(p)/x²

⇒4/(1 + x)² = 2/x²

⇒2x² = (1 + x)²

⇒2x² = 1 + x² + 2x

⇒x² - 2x - 1 = 0

⇒x = (2 ± 2√2)/2 = 1 ± √2

but x ≠ negative because x is distance.

so, x = (1 + √2) m.

Therefore third charge p is placed (1 + √2) from -2q so that it is in equilibrium.