Three infinitely long wires, each with linear charge density λ, are placed along the x-axis, the y-axis and the z-axis respectively. Which of the following denotes an equipotential surface?

Question

Accepted Answer

(1) (x²+y²)(y²+z²)(z²+x²)= constant. For an infinite line charge the potential is V=-λ/(2πε₀)ln s+ constant, where s is the perpendicular distance from the wire. Perpendicular distances from the three axes are sₓ=√y²+z², s_y=√z²+x², s_z=√x²+y². Superposing, V=-λ/(2πε₀)ln(sₓs_ys_z)=-λ/(4πε₀)ln [(y²+z²)(z²+x²)(x²+y²)]. V is constant exactly when that product is constant, so the equipotential surfaces are (x²+y²)(y²+z²)(z²+x²)= constant.

Three infinitely long wires, each with linear charge density λ, are placed along the x-axis, the y-axis and the z-axis respectively. Which of the following denotes an equipotential surface?

Step-by-step solution

Why the other options are wrong