Question

Derive an expression for the force per unit length between two long straight parallel current carrying conductors. write about the nature of force for the flow of current in (i) same direction (ii) opposite direction in parallel conductors. hence define si unit of current.

Answer 1

(i) same direction ,
Let two parallel wires of same length , current i₁ and i₂ respectively on each in same direction as shown in figure.

Magnetic field by 1st wire , B = $\bold{\frac{\mu_0i_1}{2\pi x}}$
Where x is the distance between two parallel wires .
Now, due to magnetic field creating by 1st wire , elements of 2nd wire exerts force on it .
e.g., dF = Bi₂dl = μ₀i₁i₂.dl/2πx
so, dF/dl = μ₀i₁i₂/2πx
Hence, force per unit length = μ₀i₁i₂/2πx

Now, use flaming rule ,
we observed parallel wires of current carrying same direction have attractive nature .

(ii) opposite direction ,
magnitude of force per unit length are same in both cases,
e.g., dF/dl = force per unit length = μ₀i₁i₂/2πx
But nature of force be repulsive in case of opposite direction current.