Question

The radius of a circular loop is increasing at a constant rate of 2 mm/s. The loop is placed in a
uniform magnetic field 4T and has 1000 turns, with its plane perpendicular to th

Answer 1

Correct Question:

The radius of a circular loop is increasing at a constant rate of 2 mm/s. The loop is placed in a uniform magnetic field 4T and has 1000 turns, with its plane perpendicular to the field. Find the induced EMF when radius is 1 cm.

Solution:

• As per Faraday's Law of Electromagnetic Induction, the induced EMF is equal to the rate of change of Magnetic Flux.

$EMF= \dfrac{d \phi}{d t}$

$\implies EMF= \dfrac{d (n \times B \times A)}{d t}$

$\implies EMF= nB \times \dfrac{d A}{d t}$

$\implies EMF= nB \times \dfrac{d (\pi {r}^{2} )}{d t}$

$\implies EMF= nB \times 2\pi r \times \dfrac{d r}{d t}$

$\implies EMF= 1000 \times 4 \times 2\pi (0.01) \times 0.002$

$\implies EMF= 4 \times 2\pi (0.01) \times 2$

$\implies EMF= 0.16 \times \pi$

$\implies EMF \approx \: 0.5 \: volts$

So, induced EMF is 0.5 Volts.