Two infinitely long parallel wires having linear charge densities λ1 and λ2 respectively are placed at a distance of R - Physics - Electric Charges And Fields

Question

Two infinitely long parallel wires having linear charge
densities λ1 and λ2 respectively are placed at a
distance of R metre The force per unit length on either wire will
be ?

Jyoti Pant · Accepted Answer

Suppose the infinitely long parallel wires are A and B.

We know that

the electric field due to an infinitely long straight wire A with uniform linear charge density $λ_{1}$ is

$E = \frac{λ_{1}}{2 π \in_{0} R} n o w f o r c e o n a n o t h e r w i r e B F = Q E F o r c e p e r u n i t l e n g t h = l i n e a r c h \arg e d e n s i t y o f B w i r e \times e l e c t r i c f i e l d = λ_{2} \times E = λ_{2} \times \frac{λ_{1}}{2 π \in_{0} R} = \frac{λ_{1} λ_{2}}{2 π \in_{0} R} = k \frac{2 λ_{1} λ_{2}}{R} h e r e k = \frac{1}{4 π \in_{0}}$

Two infinitely long parallel wires having linear charge densities λ1 and λ2 respectively are placed at a distance of R metre. The force per unit length on either wire will be.......?