Answer to Question #17134 in Electric Circuits for himank

Question

Two parallel current carrying conductors exert some force on each other. If the current in both conductors is doubled the force becomes k times. Find the value of k.

Answer 1

According to the Ampere's force law the force of interaction between two parallel current carrying conductors is

F1 = 2μI²/(4πr)

before doubling and

F2 = 2μ(2I)²/(4πr)

after doubling. Therefore, the coefficient k is

k = F2/F1 = 2μ(2I)²/(4πr) / (2μI²/(4πr)) = (2I)²/(I²) = 4.