Three point charges $\mathrm{q},-2 \mathrm{q}$ and 2 q are placed on x -axis at a distance $x=0, x=\frac{3}{4} R$ and $x=R$ respectively from origin as shown. If $\mathrm{q}=2 \times 10^{-6} \mathrm{C}$ and $\mathrm{R}=2 \mathrm{~cm}$, the magnitude of net force experienced by the charge $-2 q$ is ______ N.

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Electrostatics

Three point charges

q, - 2 q

and 2 q are placed on x -axis at a distance

x = 0, x = \frac{3}{4} R

and

x = R

respectively from origin as shown. If

q = 2 \times 1 0^{- 6} C

and

R = 2 cm

, the magnitude of net force experienced by the charge

- 2 q

is ______ N.

Answer: 5440

Taking the axis positions

q

x = 0

- 2 q

x = \frac{3 R}{4}

and

2 q

x = R

, the charge

- 2 q

is attracted toward the positive charge

q

on its left, giving a force

F_{1} = \frac{k q ( 2 q )}{( \frac{3 R}{4} ) ^{2}} = \frac{32 k q ^{2}}{9 R ^{2}}

directed toward the origin. It is also attracted toward

2 q

on its right, giving

F_{2} = \frac{k ( 2 q ) ( 2 q )}{( \frac{R}{4} ) ^{2}} = \frac{64 k q ^{2}}{R ^{2}}

directed away from the origin. These two forces point in opposite directions, so the net magnitude is

F = F_{2} - F_{1} = \frac{64 k q ^{2}}{R ^{2}} - \frac{32 k q ^{2}}{9 R ^{2}} = \frac{544 k q ^{2}}{9 R ^{2}}

. Substituting

k = 9 \times 1 0^{9}

q = 2 \times 1 0^{- 6}

C and

R = 2 \times 1 0^{- 2}

m gives

F = 5440

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Integer answer