A metallic rod of length l is moved perpendicular to its length with velocity v in a magnetic field B → acting perpendicular to the plane in which rod moves. Derive the expression for the induced emf.

Let a metallic rod of length l be moving perpendicular to its length with velocity v in a magnetic field B → acting perpendicular to the plane in which it moves. Let the distance covered by the rod be d s in a small amount of time d t d s = v d t Change in the flux d ϕ = B → d A where d A is change in the area through which field passes d A = l d s d A = l v d t → d ϕ = B → l v d t We know that the magnitude of induced emf is rate of change of flux ε = d ϕ d t = B → l v ∴ The emf induced in the rod is ε = B → l v

A rectangular coil of area A , having number of turns N is rotated at ‘ f ’ revolutions per second in a uniform magnetic field B , the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2 π f N B A . Or 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.

Induced emf in the coil ε = − N d ϕ d t Rate of change of flux d ϕ d t = d ( B A cos θ ) d t = − B A sin θ d θ d t d θ d t = 2 π f ∴ ε = 2 π f N B A sin θ The induced emf will be maximum when θ = 90 ∘ Maximum emf induced in the coil ε = 2 π f N B A Or (i) Induced emf in the coil ε = − N d ϕ d t Rate of change of flux d ϕ d t = d ( B A cos θ ) d t = − B A sin θ d θ d t d θ d t = 2 π f ∴ ε = 2 π f N B A sin θ The induced emf will be maximum when θ = 90 ∘ Maximum emf induced in the coil ε = 2 π f N B A (ii) Instantaneous power, P = ε 2 R = ε 0 2 R sin 2 ω t Average power dissipated per cycle, P av = ε 0 2 R < sin 2 ω t >= ε 0 2 R ⋅ 1 2 = N 2 B 2 A 2 ω 2 2 R .

A rectangular coil of area A , having number of turns N is rotated at ‘ f ’ revolutions per second in a uniform magnetic field B , the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2 π f N B A . Or 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: Power dissipation in the coil.

Induced emf in the coil ε = − N d ϕ d t Rate of change of flux d ϕ d t = d ( B A cos θ ) d t = − B A sin θ d θ d t d θ d t = 2 π f ∴ ε = 2 π f N B A sin θ The induced emf will be maximum when θ = 90 ∘ Maximum emf induced in the coil ε = 2 π f N B A Or (i) Induced emf in the coil ε = − N d ϕ d t Rate of change of flux d ϕ d t = d ( B A cos θ ) d t = − B A sin θ d θ d t d θ d t = 2 π f ∴ ε = 2 π f N B A sin θ The induced emf will be maximum when θ = 90 ∘ Maximum emf induced in the coil ε = 2 π f N B A (ii) Instantaneous power, P = ε 2 R = ε 0 2 R sin 2 ω t Average power dissipated per cycle, P av = ε 0 2 R < sin 2 ω t >= ε 0 2 R ⋅ 1 2 = N 2 B 2 A 2 ω 2 2 R .

MEDIUM

12th CBSE

IMPORTANT

Earn 100

State Faraday's laws of electromagnetic induction. Express them mathematically.

Important Questions on Electromagnetic Induction

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 6 - Electromagnetic Induction>Text Based Exercises>Q 5

State Lenz's law. Give one example to illustrate this law. The “Lenz’s law is a consequence of the law of conservation of energy”. Justify this statement.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 6 - Electromagnetic Induction>Text Based Exercises>Q 6

Describe a simple experiment (or activity) to show that the polarity of emf induced in a coil is always such that it tends to produce a current which opposes the change of magnetic flux that produces it.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 6 - Electromagnetic Induction>Text Based Exercises>Q 7

State Lenz’s law. Prove that the charge induced is independent of time.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 6 - Electromagnetic Induction>Text Based Exercises>Q 8

A metallic rod of length

l

is moved perpendicular to its length with velocity

v

in a magnetic field

\vec{B}

acting perpendicular to the plane in which rod moves. Derive the expression for the induced emf.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 6 - Electromagnetic Induction>Text Based Exercises>Q 9

Derive an expression for the induced emf produced by changing the area of a rectangular coil placed perpendicular to a magnetic field.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 6 - Electromagnetic Induction>Text Based Exercises>Q 10

A rectangular coil of area $A$ , having number of turns $N$ is rotated at ‘ $f$ ’ revolutions per second in a uniform magnetic field $B$ , the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is $2 π f N B A$ .

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.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 6 - Electromagnetic Induction>Text Based Exercises>Q 10

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: Power dissipation in the coil.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 6 - Electromagnetic Induction>Text Based Exercises>Q 11

What are eddy currents? How are these minimised? Mention two applications of eddy currents.

State Faraday's laws of electromagnetic induction. Express them mathematically.

Important Questions on Electromagnetic Induction

Learn and Prepare for any exam you want !