Question

(a ) A 14 turns circular coil is placed on a paper which lies in 1.2 T magnetic field pointing inwards to the paper. The coil's diameter changes from 22.5 cm to 7.2 cm in 1.8 s.
(i) Determine the direction of the induced current. .
(ii) Calculate the magnitude of the emf induced in the circuit.
(iii) Calculate the induced current if the circular coil resistance is 7.5 Ω

(b) A circular coil of N turns with current 9.4 mA has an inductance 15 mH. Calculate
(i) magnetic flux linkage through the coil. (ii) radius of the coil if N = 420 turns.​

Answer 1

(i) The direction of the current will be in opposite direction to the magnetic field.

(ii) The magnitude of the emf induced in the circuit is 0.359 V.

(iii) The induced current if the circular coil is 0.048 A.

b(i) The magnetic flux linkage through the coil is 1.41 x 10⁻⁴ Tm².

b(ii) The radius of the coil is r√3 m.

Direction of the current

The direction of the current will be in opposite direction to the magnetic field.

Emf induced in the circuit

Initial area of the coil = (πd²)/4

Initial area of the coil = (π x 0.225²)/4 = 0.0398 m²

Final area of the coil = (π x 0.072²)/4 = 0.001296 m²

$emf = \frac{NB(A_1 - A_2)}{t} \\\\emf = \frac{14 \times 1.2(0.0398 - 0.001296)}{1.8} \\\\emf = 0.359 \ V$

Induced current

I = emf/R

I = 0.359/7.5

I = 0.048 A

Magnetic flux linkage through the coil

Ф = LI

Ф = 0.015 x 0.0094

Ф =  1.41 x 10⁻⁴ Tm²

Radius of the coil

$L = \frac{\mu_o N^2\pi r^2}{l} \\\\r^2 = \frac{Ll}{\mu_o N^2\pi } \\\\r = \sqrt{\frac{Ll}{\mu_o N^2\pi } } \\\\r = \sqrt{\frac{0.015(l)}{4\pi\times 10^{-7} \times (420)^2 \pi } } \\\\r = 3 \sqrt{l} \ m$

where;

• l is length of the coil

Learn more about inductance of coil here: brainly.com/question/17086348