Question

A closely wound rectangular coil of 80 turns has dimensions of 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 37.0 ∘ with a magnetic field of 1.30 T to a position perpendicular to the field. The rotation takes 0.0900 s . What is the average emf EMF induced in the coil?What is the magnitude of the average emf E induced as the coil is rotated?E= ________ V

Answer 1

`E=0.2909\ V`

Step-by-step explanation:

Given:

no. of turns in the coil,
`n=80`

magnetic field, B = 1.3 T

area of the coil,
`A=(0.25* 0.4)=0.1\ m^2`

initial angle of the coil plane from the magnetic field,
`\psi_i=37^(\circ)`

final angle of the coil plane from the magnetic field,
`\psi_f=90^(\circ)`

time taken to rotate through the angle,
`dt=0.09\ s`

Now we find initial and final flux through the coil:

`\phi_i=B.A\ cos\ \psi`

`\phi_i=1.3* 0.1\ cos\ 37^(\circ)`

`\phi_i=0.1038\ Wb`

&

`\phi_f=B.A\ cos\ \psi`

`\phi_f=1.3* 0.1\ cos\ 90^(\circ)`

`\phi_f=0.13\ Wb`

`\therefore d \phi=\phi_f-\phi_i`

`d \phi=0.13-0.1038`

`d \phi=0.0262\ Wb`

Now we know according to Faraday's Law, emf induced in a coil is given by:

`E=n.(d \phi)/(dt)`

`E=80* (0.0262)/(0.09)`

`E=0.2909\ V`