JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Electrostatics

Three infinitely long wires with linear charge density

λ

are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface ?

Answer: (C)

Solution

For an infinite line charge of linear density

λ

, the potential at perpendicular distance r is

V = - 2 k λ ln r + const

.

For a wire along the z-axis, the perpendicular distance is

x^{2} + y^{2}

; adding the contributions of the three mutually perpendicular wires (along x, y and z):

V = - k λ [ln (x^{2} + y^{2}) + ln (y^{2} + z^{2}) + ln (z^{2} + x^{2})] + const

= - k λ ln [(x^{2} + y^{2}) (y^{2} + z^{2}) (z^{2} + x^{2})] + const

Setting V equal to a constant gives the equipotential surfaces as

(x^{2} + y^{2}) (y^{2} + z^{2}) (z^{2} + x^{2}) = constant

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Single correct option