A 20m wire carries a current of 15 A directed along the posi

A 2.0-m wire carries a current of 15 A directed along the positive x axis in a region where the magnetic field is uniform and given by = (3,4) T in Cartesian components. What is the resulting magnetic force on the wire?

Solution

Length L = 2 i m Where i = unit vector along positive x axis

Current I = 15 A

Magnetic field B = ( 3 i - 4 j ) x 10 ^-3 T

Resultaning magnetic force on the wire F = i ( L X B )

L X B = 2 i X ( 3 i - 4 j ) x 10 ^-3

= [ (2 x3) ( i X i ) -( 2 x 4 ) ( i X j ) ] x 10 ^-3

= 0 - 8 x k x 10 ^-3

= 0.008 k

i ( L X B ) = 15 * 0.008 k

= (0.12 k ) N