Question

a uniform magnetic field exists in a region given by b=3i+4j+5k. a rod of length 5 m is placed along y- axis is moved along x-axis with constant speed 1m/sec.the induced emf in the rod will be

Answer 1

B  = magnetic field vector = 3 i + 4 j + 5 k

L = length of rod = 0 i + 5 j + 0 k

v = velocity vector = 1 i + 0 j + 0 k

E = induced emf

induced emf is given as

E = (v x B) .L

E = ((1 i + 0 j + 0 k) x (3 i + 4 j + 5 k )) . (0 i + 5 j + 0 k)

E = (0 + 4 k - 5 j + 0 + 0 + 0 + 0 + 0 + 0 ) . (0 i + 5 j + 0 k)

E = (0 i - 5 j + 4 k). (0 i + 5 j + 0 k)

E = ((0 x 0) + (-5 x 5) + (4 x 0))

E = - 25 Volts

hence induced emf is 25 Volts