Question

a coil of and radius 2 cm carrying a current at a rate of 1.9A/s is placed coaxially inside a solenoid of 500 turns and having radius 5 cm. find the induced emf produced in the solenoida coil of and radius 2 cm carrying a current at a rate of 1.9A/s is placed coaxially inside a solenoid of 500 turns and having radius 5 cm. find the induced emf produced in the solenoid

Answer 1

Assume that $N_2=200$

$B_1=\mu_0\frac{N_1i_1}{2r_1}$

Magnetic flux linked with coil is given by

$\phi_2=N_2B_1A_2=N_2\mu_0\frac{N_1i_1}{2r_1}A_2$

According to definition of mutual inductance

$\phi_2=Mi_1 \to N_2\mu_0\frac{N_1i_1}{2r_1}A_2=Mi_1 \to M=N_2\mu_0\frac{N_1}{2r_1}A_2=$

$=N_2\mu_0\frac{N_1}{2r_1}\cdot\pi r_2^2=200\cdot4\pi \cdot10^{-7}\cdot\frac{500}{2\cdot0.05}\cdot 3.14\cdot 0.02^2=0.00158H$

$emf=M\frac{di}{dt}=0.00158\cdot 1.9\approx3mV$