Electromagnetic Induction — Practice Quiz

A Physics cheat sheet for Electromagnetic Induction — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Magnetic Flux: Flux \(\Phi\) through area \(A\) in magnetic field \(B\). \(\phi\) is angle between normal and field.

$$\Phi = BA \cos \phi$$

Faraday's Law: Induced EMF \(\mathcal{E}\) in a coil of \(N\) turns is proportional to rate of change of magnetic flux.

$$\mathcal{E} = -N \frac{\Delta \Phi}{\Delta t}$$

Motional EMF: EMF induced in a conductor of length \(L\) moving with speed \(v\) perpendicular to magnetic field \(B\).

$$\mathcal{E} = vBL$$

Electric Generator: EMF induced in a rotating coil. Peak EMF \(\mathcal{E}_0 = NAB\omega\).

$$\mathcal{E} = \mathcal{E}_0 \sin(\omega t)$$

Mutual Inductance: EMF induced in coil 2 due to changing current in coil 1. \(M\) is mutual inductance.

$$\mathcal{E}_2 = -M \frac{\Delta I_1}{\Delta t}$$

Self Inductance: EMF induced in a coil due to changing current in itself. \(L\) is self-inductance.

$$\mathcal{E} = -L \frac{\Delta I}{\Delta t}$$

Energy Stored in Inductor: Magnetic potential energy stored in an inductor carrying current \(I\).

$$Energy = \frac{1}{2} L I^2$$

Transformers: Relationship between primary (p) and secondary (s) voltages, turns, and currents.

$$\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}$$

Practice quiz

  1. A circular coil with a radius of $0.1 \text{ m}$ has $50$ turns. It is placed in a uniform magnetic field of $0.5 \text{ T}$. If the magnetic field lines are perpendicular to the plane of the coil, what is the magnetic flux through the coil?

    • A) $0.005 \pi \text{ Wb}$
    • B) $0.05 \pi \text{ Wb}$
    • C) $0.0025 \pi \text{ Wb}$
    • D) $0.01 \pi \text{ Wb}$

    Answer: A) $0.005 \pi \text{ Wb}$

  2. A coil of $200$ turns experiences a change in magnetic flux from $0.05 \text{ Wb}$ to $0.01 \text{ Wb}$ in $0.2 \text{ s}$. What is the magnitude of the average induced EMF in the coil?

    • A) $20 \text{ V}$
    • B) $40 \text{ V}$
    • C) $80 \text{ V}$
    • D) $100 \text{ V}$

    Answer: B) $40 \text{ V}$

  3. A straight conductor of length $0.5 \text{ m}$ moves at a speed of $10 \text{ m/s}$ perpendicular to a uniform magnetic field of $0.8 \text{ T}$. What is the induced motional EMF across the ends of the conductor?

    • A) $2 \text{ V}$
    • B) $4 \text{ V}$
    • C) $8 \text{ V}$
    • D) $16 \text{ V}$

    Answer: B) $4 \text{ V}$

  4. A generator coil with $100$ turns, an area of $0.1 \text{ m}^2$, rotates in a $0.2 \text{ T}$ magnetic field at an angular frequency of $50 \text{ rad/s}$. What is the peak induced EMF?

    • A) $50 \text{ V}$
    • B) $100 \text{ V}$
    • C) $200 \text{ V}$
    • D) $500 \text{ V}$

    Answer: B) $100 \text{ V}$

  5. An inductor with a self-inductance of $0.2 \text{ H}$ has a current changing at a rate of $1.5 \text{ A/s}$. What is the magnitude of the self-induced EMF across the inductor?

    • A) $0.15 \text{ V}$
    • B) $0.3 \text{ V}$
    • C) $0.6 \text{ V}$
    • D) $1.5 \text{ V}$

    Answer: B) $0.3 \text{ V}$

  6. A $0.5 \text{ H}$ inductor carries a steady current of $4 \text{ A}$. How much magnetic potential energy is stored in the inductor?

    • A) $2 \text{ J}$
    • B) $4 \text{ J}$
    • C) $8 \text{ J}$
    • D) $16 \text{ J}$

    Answer: B) $4 \text{ J}$

  7. A step-down transformer has $1000$ turns in its primary coil and $100$ turns in its secondary coil. If the primary voltage is $240 \text{ V}$, what is the secondary voltage?

    • A) $24 \text{ V}$
    • B) $240 \text{ V}$
    • C) $2400 \text{ V}$
    • D) $10 \text{ V}$

    Answer: A) $24 \text{ V}$

  8. Which of the following actions would NOT increase the magnitude of the induced EMF in a coil according to Faraday's Law?

    • A) Increasing the number of turns in the coil.
    • B) Increasing the rate at which the magnetic flux changes.
    • C) Decreasing the area of the coil.
    • D) Increasing the strength of the magnetic field.

    Answer: C) Decreasing the area of the coil.

  9. The current in a primary coil changes from $2 \text{ A}$ to $6 \text{ A}$ in $0.1 \text{ s}$. If the mutual inductance between the primary and a secondary coil is $0.05 \text{ H}$, what is the magnitude of the induced EMF in the secondary coil?

    • A) $0.2 \text{ V}$
    • B) $0.5 \text{ V}$
    • C) $2 \text{ V}$
    • D) $4 \text{ V}$

    Answer: C) $2 \text{ V}$

  10. A square loop of side $0.2 \text{ m}$ is placed in a uniform magnetic field of $0.6 \text{ T}$. The field is initially perpendicular to the loop's plane. If the field is reduced to $0.1 \text{ T}$ in $0.5 \text{ s}$, what is the magnitude of the average induced EMF in the loop?

    • A) $0.01 \text{ V}$
    • B) $0.02 \text{ V}$
    • C) $0.04 \text{ V}$
    • D) $0.08 \text{ V}$

    Answer: C) $0.04 \text{ V}$

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