Question

) A circular coil of diameter 20. cm, with 16. turns is in a 0.13 Tesla field. (a) Find the total flux through the coil when the field is perpendicular to the coil plane. (b) If the coil is rotated in 10. ms so its plane is parallel to the field, find the average induced emf.

Answer 1

a)
`\phi=0.4084\ T.m^2`

b)
`emf=653.44\ V`

Step-by-step explanation:

Given:

diameter of the coil,
`d=20\ cm=0.2\ m`

no. of turns in the coil,
`N=16`

magnetic field strength to which the coil is subjected,
`B=0.13\ T`

time taken by the coil to rotate from normal the field to parallel,
`t=10* 10^(-3)\ s`

a)

The flux through the coil can be given as:

`\phi=BA`

where:

`A=` area enclosed by the section of the coil

`\phi=0.13* \pi* (0.2^2)/(4)`

`\phi=0.4084\ T.m^2`

b)

When the coil is rotated there is change in flux which lead to an induced emf in the coil according to the Faraday's law:

`emf=N(d\phi)/(t)`

where:

`d\phi=` change in the flux

here the flux changes from maximum value to zero when the coil becomes parallel to the field lines because then there is no field line intercepting the coil area.

`emf=16* (0.4084)/(0.01)`

`emf=653.44\ V`

Answer 2

(a) 0.0041 weber

(b) 0.41 volt

Step-by-step explanation:

diameter of coil, d = 20 cm

radius of coil, r = half of diameter = 10 cm = 0.1 m

magnetic field strength, B = 0.13 tesla

(a)

The angle between the normal of the coil and the magnetic field is 0°.

Magnetic flux, Ф = B x A x Cos 0°

Ф = 0.13 x 3.14 x 0.1 x 0.1 x 1

Ф = 0.0041 Weber

(b)

angle between the magnetic field and the normal of the coil is 90°.

time, t = 10 ms = 0.01 s

final flux = B x A x cos 90° = 0

induced emf = rate of change of magnetic flux

e = (0.0041 - 0) / 0.01

e = 0.41 Volt