Two long parallel wires are separated by a distance of 2 . 50   cm . The force per unit length that each wire exerts on the other is 4 × 10 - 5   N   m - 1 , and the wires repel each other. The current in one wire is 0 . 5   A . What is the current in the second wire? (Take μ 0 = 4 π × 10 - 7 S.I. Unit)

Step-by-step solution

The formula of force between two current-carrying wire placed parallel to each other in terms of current in each wire and separation between two wires is, F = μ 0 2 π r × i 1 i 2 × l , the value is given, F l = 4 × 10 - 5   N   m - 1 , ⇒ F l = μ 0 2 π r × i 1 i 2 ⇒ i 2 = F l × μ 0 2 π r × i 1 ⇒ i 2 = 4 × 10 - 5 × 2 . 50 × 10 - 2 2 × 10 - 7 × 0 . 5 = 2 × 2 . 50 0 . 5 = 10   A