Back to Exercise: Electromagnetic Induction

Exercises: Electromagnetic Induction

Work through each section in order. Show your work where indicated.

Grade 11·20 problems·~30 min·OpenStax Physics (High School)·section·sec-20-2

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Recall / Warm-Up

What did Faraday discover in 1831 that forms the basis of electromagnetic induction?

A stationary magnetic field produces a steady electric current in a nearby conductor.

A changing magnetic field through a conducting loop induces an EMF in the loop.

A magnetic field exerts a force on a stationary charge.

A current-carrying wire creates a magnetic field around it.

Which of the following is required to induce an EMF in a conducting loop?

A strong, uniform magnetic field through the loop.

A change in the magnetic flux through the loop.

A current flowing in the loop before induction begins.

The loop must be moving — stationary loops cannot experience induction.

Magnetic flux $\Phi_B$ is defined as $\Phi_B = BA\cos\theta$ . What does $\theta$ represent in this formula?

The angle between the magnetic field and the loop's edge.

The angle between the magnetic field $B$ and the normal to the loop's surface.

The angle between the induced EMF and the current.

The angle at which the magnet approaches the loop.

Fluency Practice

Faraday's Law states that the magnitude of the induced EMF equals the rate of change of magnetic flux. Which expression is correct?

$\varepsilon = \Phi_B \cdot \Delta t$

$\varepsilon = \frac{\Delta\Phi_B}{\Delta t}$

$\varepsilon = B \cdot A$

$\varepsilon = \frac{\Delta B}{\Delta t}$

Three diagrams showing a magnetic field vector B at different angles to a loop: perpendicular to the loop (theta = 0), at 45 degrees, and parallel to the loop (theta = 90)

A square loop has sides of length $0.10\ \text{m}$ (area $A = 0.01\ \text{m}^2$ ). A uniform magnetic field of $B = 0.50\ \text{T}$ is directed perpendicular to the loop ( $\theta = 0\degree$ ). Calculate the magnetic flux through the loop in webers.

A circular loop of radius $r = 0.05\ \text{m}$ is in a magnetic field $B = 0.40\ \text{T}$ . The field makes an angle of $\theta = 60\degree$ with the normal to the loop. Calculate the magnetic flux through the loop in webers. Use $\pi \approx 3.14$ .

A rectangular loop (area $A = 0.02\ \text{m}^2$ ) is perpendicular to a magnetic field ( $\theta = 0\degree$ ). The field changes from $B_1 = 0.30\ \text{T}$ to $B_2 = 0.80\ \text{T}$ in $\Delta t = 0.25\ \text{s}$ . Calculate the magnitude of the average induced EMF in volts.

A strong permanent magnet is held stationary inside a conducting loop. The flux through the loop is large but constant. What is the induced EMF?

A large EMF proportional to $B$ , since the field is strong.

A moderate EMF proportional to $\Delta B / \Delta t$ .

Zero — the flux is not changing, so no EMF is induced.

An EMF that oscillates because the electrons in the loop respond to the field.

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