NTA Abhyas JEE Main2020PhysicsElectromagnetic InductionPractice
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
Options
- Aa b 2 c 2 ω cos ω t
- Ba b 2 c ω cos ω t
- Ca 2 b c 2 ω sin ω t
- DNone of the options
Correct answer
A. a b 2 c 2 ω cos ω t
Step-by-step solution
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