A rectangular wire loop with length a and width b lies in the x y -plane as shown. Within the loop, there is a time dependent magnetic field given by B → = c x cos ⁡ ω t i ^ + y sin ⁡ ω t k ^ .Here, c and ω are constants. The magnitude of emf induced in the loop as a function of time is

Question

A rectangular wire loop with length a and width b lies in the x y -plane as shown. Within the loop, there is a time dependent magnetic field given by B → = c x cos ⁡ ω t i ^ + y sin ⁡ ω t k ^ .Here, c and ω are constants. The magnitude of emf induced in the loop as a function of time is, a b 2 c 2 ω cos ⁡ ω t, a b 2 c ω cos ⁡ ω t, a 2 b c 2 ω sin ⁡ ω t, None of the options

MARKS App · Accepted Answer

from diagram only z component of magnetic field gives flux. Flux through small elemental area d ϕ = a d y c y sin ⁡ ω t net flux = a c sin ⁡ ω t ∫ 0 b y d y ϕ = a c b 2 2 sin ⁡ ω t ∴ Induced emf in the loop. ε = d d t ϕ m = d d t . a b 2 c 2 sin ⁡ ω t Hence, ε = a b 2 c 2 ω cos ⁡ ω t

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