A point charge of 10⁻⁸ C is placed at origin. The work done in moving a point charge 2 μC from point A(4, 4, 2) m to B(2, 2, 1) m i $s __________J.$
( 1 ────── 4πε₀ = 9 × 10⁹ in SI units)

Question

A point charge of 10⁻⁸ C is placed at origin. The work done in moving a point charge 2 μC from point A(4, 4, 2) m to B(2, 2, 1) m i $s __________J.$

( 1 ────── 4πε₀ = 9 × 10⁹ in SI units)

G1 Physics · Accepted Answer

The work done by an external agent equals the increase in electrostatic potential energy: W(ext) = ΔU. Distance of point A from the origin is r₍i₎ = √(4²+4²+2²) = √36 = 6 m. Distance of point B from the origin is r₍f₎ = √(2²+2²+1²) = √9 = 3 m. Therefore, W(ext) = kq₁q₂ [ 1 ─── r₍f₎ - 1 ─── r₍i₎]. Substitute k = 9 × 10⁹, q₁ = 10⁻⁸ C, q₂ = 2 × 10⁻⁶ C. Thus, W(ext) = 9 × 10⁹ × 10⁻⁸ × 2 × 10⁻⁶ [ 1 ─── 3 - 1 ─── 6 ] = 3 × 10⁻⁵ J = 30 × 10⁻⁶ J. Correct option: C.

A point charge of 10⁻⁸ C is placed at origin. The work done in moving a point charge 2 μC from point A(4, 4, 2) m to B(2, 2, 1) m i s __________J. ( 1 ────── 4πε₀ = 9 × 10⁹ in SI units)