Two long parallel wires separated by distance ' d ' carry currents I₁ and I₂ in the same direction. They exert a force F on each other. Now the current in one of the wire is increased to three times and its direction is made opposite. The distance between the wires is doubled. The magnitude of force between them is

Step-by-step solution

The correct option is (B). Using Ampere's circuital law, the magnetic field due to a long current carrying wire at a distance r is: B= ₀ I 2 r Force on the wire carrying current in the parallel direction is, F=I₂ B l Substituting the expression for B into the last equation and rearranging terms gives F= ₀ I₁ I₂ l 2 r For long wires, it is convenient to think in terms of F l , the force per unit length. F l = ₀ I₁ I₂ 2 r If I₂ is increased 3 times and the separation r is doubled, then F_ n e w l = 3 2 ( ₀ I₁ I₂ 2 r