Test Index

Electrostatics Part 3

Section: Physics

© examsnet.com

Question : 52 of 80

Marks: +1, -0

Three infinitely long wires with linear charge density

\lambda

are placed along the

x

y

z

-axis respectively. Which of the following denotes an equipotential surface?

[28 Jan 2025 Shift 1]

$x y+y z+z x=$ constant
$x y z=$ constant
$(x^2+y^2) (y^2+z^2) (z^2+x^2)=$ constant
$(x+y)(y+z)(z+x)=$ constant

Solution: 👈: Video Solution

Potential due to an infinite line charge at perpendicular distance

r

is

V=-2k\lambda \ln r + C

.

For a point

P(x,y,z)

, the perpendicular distances from the three wires are:

r_x=\sqrt{y^2+z^2}

r_y=\sqrt{x^2+z^2}

r_z=\sqrt{x^2+y^2}

The net potential at

P

is:

V=-2k\lambda \ln r_x-2k\lambda \ln r_y-2k\lambda \ln r_z+C

V=-2k\lambda \ln(r_x r_y r_z)+C

For an equipotential surface,

V

must be constant.

Hence

r_x r_y r_z=

constant.

Squaring both sides:

r_x^2 r_y^2 r_z^2=

constant

(y^2+z^2)(x^2+z^2)(x^2+y^2)=

constant.

This matches option C.

© examsnet.com

Go to Question:

Prev Question

Next Question