Question

draw a diagram to show the magnetic field lines produced by two parallel straight wire carrying current in the same direction.obtain the expression for the force per unit length between theses wire and define​

Answer 1

Force per unit length between 2 wires :

• Let assume that the wires are carrying current 'i' and have a length L.

• Also, let the wires be separated by distance 'd'.

In that case :

• The force experienced by one wire due to the magnetic field intensity of the other wire will be :

$F = i \times L \times B$

$\implies F = i \times L \times \dfrac{ \mu_{0}(2i) }{4\pi d}$

$\implies F = \dfrac{ \mu_{0}(2 {i}^{2} )L}{4\pi d}$

$\implies \dfrac{F}{L} = \dfrac{ \mu_{0} {i}^{2}}{2\pi d}$

$\boxed{ \implies force \: per \: unit \: length= \dfrac{ \mu_{0} {i}^{2}}{2\pi d} }$

Hope It Helps.