Question

Derive an expression for induced emf in a rod rotating in a uniform magnetic field. Draw necessary diagram.

Answer 1

$\textbf{\underline{\underline{Answer:-}}}$

Suppose the rod completes one revolution in time T.

Area swept in one rotation = πL^2

Change in flux in one rotation =B.πL^2

Now,

Induced emf =Rate of change of magnetic flux

= Change in flux / time

= B.πL^2/ T

= B.πL^2/(2π/ω)

=1/2 BL^2ω

•.• |e| = 1/2 BL^2ω

Thank you ☺

@Swigy

________________________❤

Answer 2

Answer:

An expression for induced emf in a rod rotating in a uniform magnetic field is (BR^2w)/2

Explanation:

Given

Induced Emf for a rod in uniform magnetic feild.

i.e

rod in uniform magnetic feild rotates through out circle

• So Area is given by πR^2

where,

R = radius of rod

Induced emf = change in flux / Time

• so to find induced emf we need to find change in flux and Time

Change in flux:-

change in Flux can be written as

change in flux = B x A

where,

B is magnetic field

A is area

change in flux = B × πR^2.---------->>1

Time:-

Time(t) = (2π)/omega. ------------>>>>2

substituting equation 1 and 2 in formula we get,

Induced Emf(E)=(B × πR^2)/T

=(B × πR^2)/(2π/omega)

=(BR^2w)/2

Hence,

An expression for induced emf in a rod rotating in a uniform magnetic field is (BR^2w)/2