A solenoid has 2000 turns wound over a length of 0 3 m The area of its cross section - Physics - Electromagnetic Induction

Question

A solenoid has 2000 turns wound over a length of 0 3 m The area of
its cross section is 1 2 × 10–3
m2 Around its central section a coil of 300 turns is
wound If an initial current of 2 A is reversed in 0 25 s, the e m f
induced in the coil is equal to
a) 6 x 10-4 V
b) 4 8 x 10-2 V
c) 2 4 x 10-2 V
d) 48 kV
The answer given is b please explain how i m getting c

Pintu B. · Accepted Answer

Dear Student ,
Here in this case ,
Magnetic field at the centre of the solenoid is given by ,B=μ0ni=μ0NLi=4×3·14×10-7×20000·314×2=16×10-3 TThe magnetic field is perpendicular to the plane of the coil 
Therefore ,magnetic flux linked with the coil ϕ=N'BASo the induced emf=e=-dϕdt=-ddtN'BA=-N'AdBdt=-N'A-B-Bdt=2N'BAdt⇒e=2×100×16×10-3×1×10-30·25=12·8 mV

Regards