IB Physics HL D.4 Induction questions

Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.

Type

Multiple choice Written

Difficulty

Easy Medium Hard

Question 1

Paper 2Medium8 marks

A coil rotates at constant speed in a uniform magnetic field. The same coil and field are used for both rotations; only the rotational frequency changes. Figure 1 shows the induced emf for the two rotations.

(a)

Determine the rotational frequency corresponding to each trace.

[2]

(b)

Determine the ratio of the peak induced emf in Q to that in P. Using your answer to (a), deduce the relationship between peak induced emf and rotational frequency.

[2]

(c)

Explain why increasing the rotational frequency increases the peak induced emf.

[2]

(d)

Using the relationship inferred in (b), determine the peak induced emf when the same coil rotates at $3.0\ \mathrm{Hz}$

[2]

Question 2

Paper 2Medium8 marks

A coil has 120 turns and an area of $4.0\times10^{-3}\,\text{m}^2$ It is in a uniform magnetic field of $0.20\,\text{T}$ The angle $\theta$ is measured between the field and the normal to the coil.

Initially, $\theta=60^\circ$ The coil rotates steadily until $\theta=0^\circ$ taking $0.10\,\text{s}$ The magnetic field remains constant during this rotation.

(a)

Calculate the magnetic flux through one turn of the coil initially.

[1]

(b)

Determine the magnitude of the average induced emf during the rotation.

[3]

(c)

The same rotation from $\theta=60^\circ$ to $\theta=0^\circ$ is now completed in $0.25\,\text{s}$ Calculate the magnitude of the average induced emf and explain how it compares with your answer to (b).

[2]

(d)

The coil is held stationary with its normal parallel to the field. The magnetic field decreases uniformly from $0.20\,\text{T}$ to $0.12\,\text{T}$ in $0.050\,\text{s}$ Determine the magnitude of the average induced emf.

[2]

Question 3

Multiple choiceHard1 mark

A circular loop of radius $r$ is in a uniform magnetic field of magnitude $B$ The angle between the field and the loop’s normal is $60^\circ$ The radius is changed to $2r$ the field magnitude to $B/2$ and the angle to $30^\circ$ What is the ratio of the final magnetic-flux magnitude to the initial magnetic-flux magnitude?

Show answer and explanation

Answer: C. The magnetic-flux magnitude is $\Phi=BA\cos\theta$ and the loop’s area is proportional to $r^2$ Thus

\frac{\Phi_{\mathrm{final}}}{\Phi_{\mathrm{initial}}} =\frac{1}{2}\times 4\times\frac{\cos30^\circ}{\cos60^\circ} =2\sqrt{3}.

A: reverses the ratio of the cosine factors.
B: uses the radius ratio as the area ratio, rather than squaring it.
D: omits the factor of $1/2$ from the reduced field magnitude.
Remember: the angle in the flux expression is measured from the loop’s normal.

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