Exercises: Electromagnetic Induction

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

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

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

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

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?

Magnetic flux is given by $\Phi_B = BA\cos\theta$. Complete the three cases:

When $B$ is perpendicular to the loop surface ($\theta = 0\degree$): $\Phi_B = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
When $B$ is at $45\degree$ to the normal: $\Phi_B = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
When $B$ is parallel to the loop surface ($\theta = 90\degree$): $\Phi_B = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

A bar magnet is pushed north-pole-first toward a conducting loop. As the magnet approaches, the flux through the loop increases. According to Lenz's Law, what direction does the induced current flow in the loop (as seen from the magnet's side)?

A conducting loop is near a straight wire carrying a constant DC current. The loop is then moved away from the wire (flux through the loop decreases). According to Lenz's Law, what does the induced current in the loop do?

Two scenarios: (A) A magnet with $B = 2.0\ \text{T}$ is held stationary inside a loop. (B) A magnet with $B = 0.01\ \text{T}$ is moved rapidly so that the flux through the loop changes by $0.002\ \text{Wb}$ in $0.001\ \text{s}$. Which scenario produces a larger induced EMF?

Which of the following scenarios produces electromagnetic induction in a stationary conducting loop?

A circular loop of radius $r = 0.08\ \text{m}$ lies in a plane perpendicular to a magnetic field. The field increases uniformly from $B_1 = 0.10\ \text{T}$ to $B_2 = 0.70\ \text{T}$ in $\Delta t = 0.30\ \text{s}$. Use $\pi \approx 3.14$.

Calculate the magnitude of the average induced EMF in the loop in volts. Round to three significant figures.

What is wrong with this reasoning?

What is the error in this explanation of Lenz's Law?

A generator consists of a square coil with $N = 100$ turns, each of side length $0.10\ \text{m}$ (area per turn $= 0.01\ \text{m}^2$). The coil is in a magnetic field of $B = 0.50\ \text{T}$. The coil rotates from $\theta = 0\degree$ to $\theta = 90\degree$ in $\Delta t = 0.050\ \text{s}$.

Calculate the magnitude of the average induced EMF for all 100 turns combined, in volts.

Explain how a transformer works using Faraday's Law, and why a transformer only works with AC (alternating current) and not with DC (direct current). Your answer should mention the primary coil, secondary coil, magnetic flux, and the word "changing."