Question

changing a magnetic field B induces an emf ϵ in a coil of radius R. What is the induced emf in the coil of radius 2R?
Select one:
2ϵ
ϵ
4ϵ
8ϵ

Answer 1

Answer:

Exp  lnduced emf formula

Faraday's law of induction states that the EMF induced by a change in magnetic flux is EMF=−NΔΦΔt EMF = − N Δ Φ Δ t , when flux changes by Δ in a time Δtanation:

Answer 2

Answer:

The induced emf in the coil of radius 2R is 4e i.e.option(3).

Explanation:

From Faraday's law of electromagnetic induction we have;

$e=-\frac{d\phi}{dt}$       (1)

Where,

e=induced emf

dФ=change in magnetic flux

dt=change in time

Also,

dФ=B.A

B=magnetic field

A=area in which the magnetic field is present

By substituting the value of dФ in equation (1) we get;

$e=-\frac{B.A}{dt}$    (2)

From the question we have,

e₁=e

R₁=R

R₂=2R

By placing the required values in equation (2) we get;

$\frac{e_1}{e_2}=\frac{-\frac{B.A_1}{dt}}{-\frac{B.A_2}{dt}}=\frac{A_1}{A_2}$          (3)

The area of the coil is given as πr².      (r=radius of the coil)

So,

$\frac{e}{e_2}=\frac{\pi\times R^2}{\pi\times (2R)^2}=\frac{1}{4}$

$e_2=4e$           (4)

Hence,  the induced emf in the coil of radius 2R is 4e i.e.option(3).