Question

Three long, straight, parallel wires carrying different currents are arranged as shown in the diagram. In the given arrangement, let the net force per unit length on the wire C be F. If the wire B is removed without disturbing the other two wires, then the force per unit length on wire A is:

• A. -F
• B. 3F
• C. 2F
• D. -3F

Answer 1

Answer: (D)

-3F

Answer 2

The correct option is: (D): -3F.

Wire C is between wires A and B, and it is influenced by the magnetic fields generated by both wires A and B. If the net force per unit length on wire C is F, it means that the magnetic forces due to wires A and B are balanced, resulting in no net force on wire C.

Now, when you remove wire B while keeping wire A and C in place, the situation changes. The magnetic field produced by wire A still affects wire C, and since wire B is removed, there's no longer a balancing magnetic field from wire B.

Without wire B, there's now an imbalance in the magnetic forces acting on wire C due to the unopposed influence of wire A. This results in a net force per unit length on wire C, which we can call -F (since it's in the opposite direction to the original balancing force F).

This unopposed force from wire A on wire C also leads to an equal and opposite force on wire A itself, as per Newton's third law of action and reaction. So, the force per unit length on wire A will be -F. Since the initial force on wire C was F, the force on wire A is -3F (-F due to its own magnetic field and -2F due to the absence of the counterbalancing force from wire B).

Therefore, the answer of -3F is justified based on the change in the magnetic forces and the principles of Ampère's law and Newton's third law.