Two parallel wires I and II that are near each other carry currents i and 3i both in the same direction. Compare the forces that the two wires exert on each other. A. The wires exert equal magnitude attractive forces on each other. B. Wire I exerts a stronger force on wire II than II exerts on I. C. Wire II exerts a stronger force on wire I than I exerts on II. D. The wires exert equal magnitude repulsive forces on each other. E. The wires exert no forces on each other.

A. The wires exert equal magnitude attractive forces on each other.

Explanation:

Magnetic field due to current i on current 2i

B₁ = 10⁻⁷ x 2 i / r where r is distance between the two wires

Force on wire II due to wire I per unit length

= magnetic field x current in wire II

= B₁ x 2 i

= [ 10⁻⁷ x 2 i / r ]  x 2i

= 4  x 10⁻⁷ i² / r

Magnetic field due to current 2i on current i

B₂ = 10⁻⁷ x 4 i / r where r is distance between the two wires

Force on wire I due to wire II per unit length

= magnetic field x current in wire I

= B₂ x  i

= [ 10⁻⁷ x 4 i / r ]  x i

= 4  x 10⁻⁷ i² / r

So final forces on each wire are same .

This force will be attractive in nature . The direction of force can be known from fleming's right  hand rule .