Electromagnetic Induction: Key Formulas
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Questions and Answers

Magnetic flux equals:

  • $U_m = \frac{1}{2} L I^2 = -\Phi I$
  • $\varepsilon = -N \frac{\Delta \Phi}{\Delta t}$
  • $B = B \cdot A = BA \cos \theta$ (correct)
  • $L = \mu_0 \mu_r n^2 A l$

What is the formula for induced emf in a coil?

$\varepsilon = -N \frac{\Delta \Phi}{\Delta t}$

What is the formula for EMF induced in a moving conductor?

$\varepsilon = Bvl$

If L is self inductance, emf induced $\varepsilon = -L \frac{\Delta I}{\Delta t}$, where L is the coefficient of ______

<p>self-induction</p> Signup and view all the answers

What is the self inductance equation for a solenoid?

<p>$L = \mu_0 \mu_r n^2 A l = \mu_0 \mu_r \frac{N^2 A}{l}$</p> Signup and view all the answers

What is the equation for Mutual Inductance?

<p>$E = -M \frac{\Delta I}{\Delta t}$</p> Signup and view all the answers

What is the mutual inductance equation for a solenoid coil system?

<p>$M = \mu_0 \frac{N_1 N_2 A}{l}$</p> Signup and view all the answers

What is the equation for energy stored in inductance?

<p>$U_m = \frac{1}{2} L I^2 = -\Phi I$</p> Signup and view all the answers

Match the Primary Current with the Induced Current:

<p>Current increasing = Clockwise current Current decreasing = Anticlockwise current Key is pressed = Opposite to direction of main currents Key is Released = In the direction of main current</p> Signup and view all the answers

Whenever the flux linked with a circuit changes, there is an induced emf in the circuit. This emf in the circuit lasts:

<p>as long as the magnetic flux in the circuit changes. (C)</p> Signup and view all the answers

An area A = 0.5 m shown in the figure is situated in a uniform magnetic field B = 4.0 Wb/m and its normal makes an angle of 60 with the field. The magnetic flux passing through the area A would be equal to

<p>1.0 weber (C)</p> Signup and view all the answers

A square of side L meters lies in the X-Y plane in a region, where the magnetic field is given by $B = B_0(2\hat{i} + 3\hat{j} + 4\hat{k}) T$, where $B_0$ is constant. The magnitude of flux passing through the square is:

<p>$4 B_0 L^2$ Wb (B)</p> Signup and view all the answers

A loop, made of straight edges has six corners at A(0, 0, 0), B(L, O, 0), C(L, L, 0), D(0, L, 0) E(0, L, L) and F(0, 0, L). A magnetic field $B = B_0(\hat{i} + \hat{k}) T$ is present in the region. The flux passing through the loop ABCDEFA (in that order) is

<p>$2 B_0 L^2$ Wb (C)</p> Signup and view all the answers

An emf is produced in a coil, which is not connected to an external voltage source. This can be due to:

<p>all of the above. (D)</p> Signup and view all the answers

Flashcards

Magnetic Flux

The amount of magnetic field lines passing through a given area.

Induced EMF

The emf generated in a circuit due to a changing magnetic flux.

EMF in Moving Conductor

EMF produced in a conductor moving through a magnetic field.

Self-Inductance (L)

The property of a coil to oppose changes in current.

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EMF and Self-Inductance

The induced EMF due to self-inductance when current changes.

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Self-Inductance of Solenoid

The inductance of a solenoid based on its physical characteristics.

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Mutual Inductance (M)

The induction of EMF in one coil due to changing current in another.

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Mutual Solenoid Inductance

Mutual inductance depends on turns, area, and length of coils.

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Energy in Inductance

Energy stored in an inductor due to its magnetic field.

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Lenz's Law

Direction of induced current opposes the change causing it.

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Inductance Role

Parameter that opposes changes in current; the electrical equivalent of mass/inertia.

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Electromagnetic induction

Faraday's Law principle

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Duration of induced EMF

Induced emf only lasts as long as the magnetic flux changes

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Magnetic Flux Calculation

Magnetic flux equals the magnetic field strength times the area

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How to produce and EMF

The coil is in a time varying magnetic field or it is moving in a magnetic field (varying or constant).

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Acceleration of falling magnet

It will be less than that due to gravity.

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Charge Flowing through the galvanometer

The ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is $A B / R$.

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Self inductance of Solenoid

As $l$ decreases and A increases.

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Inductance Changes

The inductance $L$ of a solenoid will increase as the length decreases and the area increases.

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Oscillating metallic pendulum in magnetic field

The oscillating metallic pendulum in a uniform magnetic field directed perpendicular to the plane of oscillation slows down.

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Small magnet falling through metallic cylinder

A metallic cylinder is held vertically and then a small magnet is dropped along its axis. It will fall with acceleration $a<g$.

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Force Direction

The induced field will generate a force which opposes it.

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Moves With a Uniform Velocity

A conducting square loop of side $L$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of it's sides is$\frac{B l v}{R}$

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Two Circular Coils

Mutual inductance will be maximum in situation (i).

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Short Bar Magnet

If a short bar magnet is moved along coil axis the induced EMF (E) will change from - to + and back to -.

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Induced Electric Field

The magnitude of the induced electric field at point $P$ at a distance $\mathrm{r}$ from the centre of the circular region increases as $r$.

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Metal Rotating Rod

A metal rod $O A$ is pivoted at the centre $O$ of the loop. The other end $A$ of the rod touches the loop. The rod $O A$ and the loop are resistanceless. The current induced in the tungsten wire is $\frac{B \omega a}{2 R}$

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Time Varying Magnetic Field

A coil of area $5.0 \times 10^{-3} \mathrm{~m}^{2}$ is a coil placed perpendicular to a time varying magnetic field shown in figure. The value of induced emf in coil in $10 \mathrm{~ms}$ is: 0-1$\mathrm{V}$

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Self-Inductance of the coil

When the current changes from + 2A to -2 A in 0.05 s, an emf of 8 V is induced in a coil. The coefficient of self-inductance of the coil is 0-1$\mathrm{H}$

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Effective Inductance

The effective inductance between $$\mathrm{A}$ and $$\mathrm{B}$ is 1.5H

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Study Notes

  • Electromagnetic induction involves several important formulas and concepts

Magnetic Flux

  • Magnetic Flux is given by B.A or BA cos θ, where θ is the angle between the area vector A and the magnetic field B

Induced EMF in a Coil

  • Induced electromotive force (EMF) in a coil: ε = -N (ΔΦ/Δt)
  • N represents the number of turns in the coil
  • ΔΦ/Δt represents rate of change of magnetic flux

EMF in a Moving Conductor

  • EMF induced in a moving conductor: ε = Bvl
  • B, v, and l are mutually perpendicular

Magnetic Flux and Self-Induction

  • Magnetic flux is given as Φ = LI, where L denotes the coefficient of self-induction

Self-Inductance and EMF

  • If L represents self-inductance, induced EMF is given as ε = -L(ΔI/Δt), where ΔI/Δt denotes the rate of change of current

Self-Inductance of a Solenoid

  • Self-inductance of a solenoid: L = μ₀μᵣN²A/ l = μ₀μᵣn²Al
  • N: total number of turns, n: number of turns per unit length, A: cross-sectional area, l: length of the solenoid, μ₀: permeability of free space and μᵣ: relative permeability

Mutual Inductance

  • Mutual inductance is given as ε = -M(ΔI/Δt)
  • M denoted the mutual inductance and ΔI/Δt the rate of change of current

Mutual Inductance of a Solenoid Coil System

  • Mutual inductance of a solenoid coil system: M = μ₀N₁N₂A / l
  • N₁ is the number of turns per meter in the solenoid
  • N₂ denotes number of turns in the coil
  • l: length of the system

Energy Stored in an Inductance

  • Energy stored in an inductance: Uₘ = (1/2)LI² = (1/2)ΦI where L is inductance, I current and Φ is magnetic flux

Direction of Induced Current

  • Straight wire-coil system:
  • Current increasing results in a clockwise induced current.
  • Current decreasing results in an anticlockwise induced current
  • Self-inductive circuit:
  • Key pressed results in an induced current opposite to the direction of the main current
  • Key released results in an induced current in the direction of the main current

Magnetic-Coil System

  • North pole approaching coil induces an anticlockwise current.
  • North pole receding coil induces a clockwise current

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Electromagnetic Induction PDF - Physics Questions and Answers

Description

Explore the fundamental formulas of electromagnetic induction, including magnetic flux, induced EMF in coils and moving conductors, self-inductance, and the self-inductance of a solenoid. Understand how these concepts relate to changing magnetic fields and induced currents. Learn about Faraday's Law and Lenz's Law.

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