JEE Main202528 Jan 2025Morning ShiftPhysicsElectrostaticsActual
Three infinitely long wires with linear charge density are placed along the x-a x i s, y -axis and z- axis respectively. Which of the following denotes an equipotential surface?
Options
- Ax y z= constant
- Bx y+y z+z x= constant
- C(x^2+y^2 ) (y^2+z^2 ) (z^2+x^2 )= constant
- D(x+y)(y+z)(z+x)= constant
Correct answer
C. (x^2+y^2 ) (y^2+z^2 ) (z^2+x^2 )= constant
Step-by-step solution
Potential due to an infinite wire is V=2 k r , where r is the distance from the wire. Taking the point in space P(x, y, z) Distance from wire along x -axis is r_x= y^2+z^2 Distance from wire along y -axis is r_y= x^2+z^2 Distance from wire along z -axis is r_z= x^2+y^2 Potential at P due to wire along x -axis is V_x=2 k r_x Potential at P due to wire along y -axis is V_y=2 k r_y Potential at P due to wire along z -axis is V_z=2 k r_z Not potential at P=V=V_x+V_y+V_z or V=2 k r_x+2 k r_y+2 k r_z i.e. V=2 k (r_x r_y