# Answer to Question #17424 in Electric Circuits for Prince Ram

Question #17424

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

Expert's answer

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.

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.

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