A long rigid wire lies along the X - axis and carries a current of 10 A in the positive X - direction. Round the wire, the external magnetic field is B → = i ^ + 2 x 2 j ^ with x in meters and B in Tesla. The magnetic force (in S I units) on the segment of the wire between x = 1 m and x = 4 m is

Step-by-step solution

d F → = I d l → × B → F = I ∫ d x i ^ × i ^ + 2 x 2 j ^ = 10 ∫ x = 1 x = 4 2 x 2 d x k ^ = 20 x 3 3 x = 1 x = 4 = 20 3 4 3 - 1 3 = 420 N d F → = I ( d l → × B → ) F = I ∫ ( d x i ^ ) × ( i ^ + 2 x 2 j ^ ) = 10 ∫ x = 1 x = 4 2 x 2 d x k ^ = 20 [ x 3 3 ] x = 1 x = 4 = 20 3 [ 4 3 - 1 3 ] = 420 N