Question

A circular coil of 185 turns and radius 4.50 cm is placed inside and coaxial to a solenoid with 350 turns/m. If the current in the solenoid is represented by the equation I = a(1 − e−bt) where a = 12.5 A and b = 2.10 s−1, determine the magnitude of the induced emf in the coil when t = 1.50 s.

Answer 1

Answer:

Magnitude of the induced emf is 11.62 V

Explanation:

Given:

No. of turns of the circular coil, N=185

Radius, R=4.50 cm=0.045 m

No. of turns of solenoid per meter(m), n=350

a=12.5 A

b=2.10 $s^{-1}$

Now,

To determine the emf induced in the coil at t = 1.50 s:

The given equation is:

$I=a(1-e^{-bt})$

Now,

$B=\mu_{o}nI=\mu_{o}na(1-e^{-bt})$

$\frac{dB}{dt}=\mu_{o}nabe^{-bt}$

Now, substituting the respective values:

$\frac{dB}{dt}=-4\pi\times 10^{-7}\times 350\times 12.5\times 2.10e^{-2.10\times 1.50}$

$\frac{dB}{dt}=0.988\ T/s$

Now,

$emf=NA\frac{dB}{dt}$

where,

A=Area=$\pi R^{2}$

Thus,

$emf=185\times \pi\times (4.50\times 10^{-2})^{2}\times 11.545e^{-3.15}$

$emf=11.62 V$