A point charge of $10^{-8} \mathrm{C}$ is placed at origin. The work done in moving a point charge $2 \mu \mathrm{C}$ from point $\mathrm{A}(4,4,2) \mathrm{m}$ to $\mathrm{B}(2,2,1) \mathrm{m}$ is ______ J. ($\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9}$ in SI units)

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Electrostatics

A point charge of

1 0^{- 8} C

is placed at origin. The work done in moving a point charge

2 μ C

from point

A (4, 4, 2) m

B (2, 2, 1) m

is ______ J.
(

\frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9}

in SI units)

Answer: (C)

The work equals the change in potential energy,

W = k q_{1} q_{2} (\frac{1}{r _{B}} - \frac{1}{r _{A}})

. Here

r_{A} = 4^{2} + 4^{2} + 2^{2} = 6 m

and

r_{B} = 2^{2} + 2^{2} + 1^{2} = 3 m

. Thus

W = 9 \times 1 0^{9} \times 1 0^{- 8} \times 2 \times 1 0^{- 6} (\frac{1}{3} - \frac{1}{6}) = 1.8 \times 1 0^{- 4} \times \frac{1}{6} = 30 \times 1 0^{- 6} J

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Single correct option