MHTCET 15 May 2024 Shift 2 Paper

Concept:Parallel wires carrying currents in the same direction attract each other, while currents in opposite directions repel each other.The magnetic force per unit length is proportional to the product of the currents and inversely proportional to the separation between the wires.Explanation:From the figure, wire A and wire C are on two sides of wire B.Wire A carries current $I$, wire B also carries current $I$, and wire C carries current $3I$.Since currents in A and B are in the same direction, wire B is attracted towards wire A.Since currents in B and C are in opposite directions, wire B is repelled by wire C, which also pushes it towards wire A.The magnitude of force due to A is:$$F_{AB}=\frac{\mu_0 I^2 L}{2\pi d}$$The magnitude of force due to C is:$$F_{CB}=\frac{3\mu_0 I^2 L}{2\pi d}$$Both forces act on wire B in the same direction, i.e. towards wire A.Hence the resultant force is directed towards wire A.Answer:The resultant force on wire B is directed towards wire A.