Question

A wire of length 4m placed normal to the magnetic
field of (2i+4j) tesla is moving with a velocity(4i+6j+8k)
The emf induced across the ends
of the wire will be
(1) 4 V
(2) 8 v
(3) 16 V
(4) 32 V​

Answer 1

answer : option (3) 16volts

explanation : induced emf , $\xi$ = $(v\times B)$L

here it is given that wire of length 4m is normal to the plane of magnetic field.

so, L = 4k

also, given, B = (2i + 4j) Tesla

v = (4i + 6j + 8k) m/s

= [(4i + 6j + 8k) × (2i + 4j + 0k)]. 4k

= [i (6 × 0 - 8 × 4) - j(4 × 0 - 8 × 2) + k(4 × 4 - 6 × 2) ] × 4

= [-32i + 16j + 4k ]. 4k

= 16 Volts

hence, option (3) is correct choice.