Question

A uniform magnetic field is directed at an angle of 30o with the plane of a circular coil of radius 4cm and 1000 turns. The magnetic field changes at a rate of 5 T per second. Calculate the following:

a. Area vector
b. Induced emf

Answer 1

(a) The area vector is 0.00503 m² at 30⁰ from the magnetic field

(b) The induced emf is 12.58 V

Step-by-step explanation:

Given;

angle between the magnetic field and the plane of the circular coil, = 30⁰

number of turns of the coil, N = 1000

radius of the coil, r = 4 cm = 0.04 m

change in the magnetic field with time, dB/dt = 5 T/s

(a) The area vector is calculated as;

A = πr²

A = π x (0.04)²

A = 0.00503 m²

The area vector is 0.00503 m² at 30⁰ from the magnetic field.

(b) The induced emf is calculated as;

`emf = N(\Delta \phi)/(\Delta t) \\\\where;\\\\\phi = BAcos \theta\\\\emf = N* (dB)/(dt) * Acos (\theta)\\\\where;\\\\\theta \ is \ the \ angle \ between \ a \ perpendicular \ vector \ to \ the \ area\\ and\ the \ magnetic\ field\\\\\theta = 90 - 30 = 60^0\\\\emf = N* (dB)/(dt) * Acos (\theta)\\\\emf = (1000) * (5 )* (0.00503) * cos (60)\\\\emf = 12.58 \ V`