Question

A point charge Q is located a distance d away from the center of a very long charged wire. The wire has length L >> d and total charge q. What force does the wire experience?

Answer 1

Answer:

$F = \frac{Qq}{2\pi \epsilon_0 L d}$

Explanation:

As we know that if a charge q is distributed uniformly on the line then its linear charge density is given by

$\lambda = \frac{q}{L}$

now the electric field due to long line charge at a distance d from it is given as

$E = \frac{2k\lambda}{d}$

$E = \frac{q}{2\pi \epsilon_0 d}$

now the force on the other charge in this electric field is given as

$F = QE$

$F = \frac{Qq}{2\pi \epsilon_0 L d}$