A wheel with 10 metallic spokes each 0.5 m long is rotated with angular speed of 120 revolutions per minute in a plane normal to the earth's magnetic field. If the earth's magnetic field at the given place is 0.4 gauss, find the EMF induced between the axle and the rim of the wheel.

Solution

Given,
A wheel with 10 metallic spokes.
Length of metallic spoke = 0.5 m
Angular speed of the wheel = 120 rev/min
Earth's magnetic field, B =0.4 G

The area covered by an angle θ,

A = {πr}^{2} \frac{θ}{2 π} = \frac{r^{2}}{2} θ

The induced EMF,

|E| = \frac{dϕ}{dt} = \frac{d (BA)}{dt} = B \frac{r^{2}}{2} \frac{dθ}{dt} = B \frac{r^{2}}{2} ω

ν = 120 rev / \min = 2 rev / s ω = 2 πν = 4 π rad / s r = 0.5 m B = 0.4 G = 0.4 \times 10^{- 4} T

Therefore,

Induced emf is given by,

E = \frac{1}{2} {Br}^{2} ω

E = \frac{2 π \times 2 \times 0.4 \times 10^{- 4} \times {(0.5)}^{2}}{2}

= 6.28 \times 10^{- 5} V

Each spoke will act as a parallel source of EMF.

Hence, the EMF will be 6.28 x 10^–5 V.

For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

A wheel with 10 metallic spokes each 0.5 m long is rotated with angular speed of 120 revolutions per minute in a plane normal to the earth's magnetic field. If the earth's magnetic field at the given place is 0.4 gauss, find the EMF induced between the axle and the rim of the wheel.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

A wheel with 10 metallic spokes each 0.5 m long is rotated with angular speed of 120 revolutions per minute in a plane normal to the earth's magnetic field. If the earth's magnetic field at the given place is 0.4 gauss, find the EMF induced between the axle and the rim of the wheel.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?