Question

Two parallel wires, each carrying a current I, repel each other with a force F. If both currents are doubled, the force of repulsion is

(A) 2F 

(B) 2√2 F 

(C) 4F 

(C) 4√2 F 

(E) 8F

Answer 1

The correct option is: (C) 4F 

Explanation:

Due to action reaction the forces must be the same. Another way to look at it is that wire A creates the field that wire B is sitting in based on its current I, B_a = μ_oI_a / 2πR. The force on wire B is dependent on the field from A, and also the current in wire B itself and is given by F_b=B_aI_bL F_b = (μ_oI_a / 2πR) I_b L. So since both currents from A and B affect each respective force, they should share the same force., the force on either wire is F_b = (μ_oI_a / 2πR) I_bL. So doubling both I’s in the equation gives 4x the force.