A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s^–1 in a uniform horizontal magnetic field of magnitude 3 x 10^–2 T. Obtain the maximum and average e.m.f. induced in the coil. If the coil forms a closed loop of resistance 10 Ω, calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?

Solution

Given,
Radius of the coil, r = 8 cm
Number of turns in the coil, N = 20
Therefore, flux through each turn,

ϕ = \vec{B} \vec{A} = BA \cos θ

ϕ = {Bπr}^{2} \cos (ωt)

For N turns,

ϕ_{T} = NB {πr}^{2} \cos (ωt)

Thus, induced e.m.f,

|ε| = \frac{{dϕ}_{T}}{dt}

= \frac{d [NB {πr}^{2} \cos (ωt)]}{dt}

|ε| = \frac{{dϕ}_{T}}{dt}

= \frac{d [N B {πr}^{2} \cos (ωt)]}{dt}

|ε| = NB {πr}^{2} ω \sin (ωt)

The maximum e.m.f,

ε_{0} = NB {πr}^{2} ω = 20 \times 50 \times π \times 64 \times 10^{- 4} \times 3.0 \times 10^{- 2}

= 0.603 V

The average e.m.f, over a cycle = 0
Resistance of the closed loop formed by the coil, R = 10 Ω
The maximum current,

I_{0} = \frac{ε}{R} = \frac{0.603}{10} = 0.0603 A

Power loss,

P = \frac{1}{2} E_{0} I_{0} = \frac{1}{2} \times 0.603 \times 0.0603 = 0.018 W

The induced current causes a restoring torque in the coil. An external source is responsible for the supply of energy for this torque. So we can say that source of this power is the external rotor.

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?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

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?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

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?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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?