JEE Main2017PhysicsElectromagnetic InductionActual
A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b . The two loops are in the same plane. The outer loop of radius b carries an alternating current I = I 0 cos ⁡ ω t . The emf induced in the smaller inner loop is nearly:
Options
- Aπ μ 0 I 0 a 2 b ω sin ω t
- Bπ μ 0 I 0 2 . a 2 b ω cos ω t
- Cπ μ 0 I 0 b 2 a ω cos ω t
- Dπ μ 0 I 0 2 . a 2 b ω sin ω t
Correct answer
D. π μ 0 I 0 2 . a 2 b ω sin ω t
Step-by-step solution
Induced emf, ε = M d I d t , Current is given as, I = I 0 c o s ω t   M = μ 0 π a 2 2 b ,   ε = - M d d t   ( I 0 cos ω t ) c = M   ω I 0   sin ω t = μ 0 π a 2 2 b ω   I 0 sin ⁡   ω t