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Electric Charges And Fields

Question

A coil of number of turns N, area A, is rotated at a constant angular speed ω, in a uniform magnetic field B, and connected to a resistor R. Deduce expressions for:
(i) maximum emf induced in the coil.
(ii) power dissipation in the coil.

Solution

Given, a coil of N turns having an area A, rotated with angular speed ' $ω$ ' in a uniform magnetic field 'B' connected to a resistor 'R' .

The flux linking to the coil, $ϕ = NBA \sin (ωt)$
Therefore,
Induced EMF, $E = \frac{d (NBA \cos ωt)}{dt} = NBA ω \sin ωt$

When, sin $ω$ t = $\pm$ 1, the induced emf value is maximum.

(i) The maximum EMF, $E_{0} = NBA ω$

(ii) The power dissipated in the coil is given by,
$P = \frac{{E^{2}}_{rms}}{R} = \frac{E_{0}^{2}}{2 R} = \frac{(NAB ω)^{2}}{2 R}$

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?

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Electric Charges And Fields

A coil of number of turns N, area A, is rotated at a constant angular speed ω, in a uniform magnetic field B, and connected to a resistor R. Deduce expressions for:
(i) maximum emf induced in the coil.
(ii) power dissipation in the coil.

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?

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

A coil of number of turns N, area A, is rotated at a constant angular speed ω, in a uniform magnetic field B, and connected to a resistor R. Deduce expressions for:(i) maximum emf induced in the coil.(ii) power dissipation in the coil.

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 coil of number of turns N, area A, is rotated at a constant angular speed ω, in a uniform magnetic field B, and connected to a resistor R. Deduce expressions for:
(i) maximum emf induced in the coil.
(ii) power dissipation in the coil.

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?