Question

Two long wires having linear charge densities λ1 and λ2 are placed perpendicular to each other at separation r. The electrostatic force of interaction between them is proportional to r^n. Then value of n is

Answer 1

Given:

Two long wires having linear charge densities λ1 and λ2 are placed perpendicular to each other at separation r.

To find:

Value for 'n' when electrostatic force of interaction between them is proportional to r^n.

Calculation:

• Since both the wires are considered to be infinite, the force experienced by any one of the wires will be :

$\rm \: F = E_{1} \times q_{2}$

$\rm \implies\: F = \dfrac{2k \lambda_{1}}{r} \times \lambda_{2}(l)$

• 'k' is Coulomb's Constant, 'l' is length of the wires.

$\rm \implies\: F = \dfrac{2k \lambda_{1} \lambda_{2}l }{r}$

$\rm \implies\: F \propto \: {r}^{ - 1}$

$\rm \implies\: F \propto \: {r}^{ n}$

So, value of n is -1.