Electromagnetic induction

A small coil of wire lies in a non-uniform magnetic field, as illustrated in Fig. 10.1. The coil contains 40 turns of wire and travels in a straight line at constant speed. Its displacement from a fixed point $P$ is $x$. Fig. 10.2 shows how the magnetic flux $\phi$ in the coil varies with $x$.

Feb/March 2016

Fig. 9.1 shows an ideal transformer.

Feb/March 2017

Define the term magnetic flux.

Feb/March 2018

Fig. 10.1 shows a cross-section of a solenoid carrying current.

Feb/March 2019

What does magnetic flux linkage mean?

Feb/March 2021

A small solenoid with a cross-sectional area of $1.6 \times 10^{-3}\,\text{m}^2$ is located inside a larger solenoid with a cross-sectional area of $6.4 \times 10^{-3}\,\text{m}^2$, as shown in Fig. 6.1. The larger solenoid has $600$ turns and is connected to a d.c. power supply so that it produces a magnetic field. The smaller solenoid has $3000$ turns.

Feb/March 2022

Coil C is a small coil with 64 turns and a cross-sectional area of $0.71\,\text{cm}^2$. It sits inside a solenoid, as shown in Fig. 6.1. The centre of coil C lies on the solenoid’s central axis.

Feb/March 2024

State Faraday’s law for electromagnetic induction.

Feb/March 2025

A transformer is shown in Fig. 6.1.

May/June 2011

A bar magnet hangs vertically from the free end of a helical spring, as shown in Fig. 5.1. One pole of the magnet lies inside a coil. The coil is joined in series to a high-resistance voltmeter. The magnet is pulled vertically and then released. Fig. 5.2 shows how the voltmeter reading V changes with time t.

May/June 2011

A bar magnet hangs vertically from the free end of a helical spring, as shown in Fig. 5.1. One pole of the magnet lies inside a coil. The coil is connected in series with a high-resistance voltmeter. The magnet is moved vertically and then let go. The change in the voltmeter reading V with time t is shown in Fig. 5.2.

May/June 2011

Define the tesla in terms of magnetic flux density.

May/June 2013

A basic transformer is shown in Fig. 6.1.

May/June 2013

Define the tesla in terms of the force on a current-carrying conductor in a magnetic field.

May/June 2013

A straightforward transformer is shown in Fig. 6.1.

May/June 2013

A solenoid is wired in series with a battery and a switch. A Hall probe is positioned near one end of the solenoid, as shown in Fig. 7.1. The current in the solenoid is turned on. The Hall probe is then moved until the reading is at its greatest. The current is later turned off.

May/June 2014

A solenoid is connected in series to a battery and a switch. A Hall probe is positioned near one end of the solenoid, as shown in Fig. 7.1. The current in the solenoid is switched on. The Hall probe is moved until the reading is at its greatest. The current is then switched off.

May/June 2014

A solenoid is joined in series with a resistor, as shown in Fig. 7.1. While the magnet is moved into the solenoid, thermal energy is transferred to the resistor. Use laws of electromagnetic induction to explain where this thermal energy comes from.

May/June 2015

A coil of insulated wire is wrapped around a copper core, as shown in Fig. 10.1. An alternating current flows through the coil. The heating effect produced by the current in the coil is negligible.

May/June 2016

As shown in Fig. 10.1, coils P and Q are positioned close together.

May/June 2016

A coil of insulated wire is wound around a copper core, as shown in Fig. 10.1. An alternating current is passed through the coil. The heating effect of the current in the coil is negligible. Explain why the temperature of the core rises.

May/June 2016

A comparator circuit is intended to turn on a mains lamp when the ambient light level reaches a chosen value. Figure 6.1 shows an incomplete version of the circuit.

May/June 2017

Fig. 9.1 shows a simple transformer.

May/June 2017

The comparator circuit is intended to turn on a mains lamp once the ambient light level reaches a chosen value. Fig. 6.1 shows an incomplete diagram of the circuit.

May/June 2017

A simple transformer is shown in Fig. 9.1.

May/June 2017

State Faraday’s law for electromagnetic induction.

May/June 2018

State the meaning of the magnetic flux linkage of a coil.

May/June 2018

State Faraday’s law for electromagnetic induction.

May/June 2018

A solenoid is linked in series to a battery and a switch, as shown in Fig. 8.1. A small coil, connected to a sensitive ammeter, is placed close to one end of the solenoid. When the current in the solenoid is switched on, the magnetic field inside the solenoid changes.

May/June 2019

State Faraday’s law that describes electromagnetic induction.

May/June 2019

As shown in Fig. 8.1, a battery and a switch are connected in series with a solenoid. Near one end of the solenoid is a small coil linked to a sensitive ammeter. When the solenoid current is switched on, the magnetic field inside the solenoid changes.

May/June 2019

A wire coil lies in a uniform magnetic field of flux density $B$. The coil is $3.6\,\text{cm}$ in diameter and is made of $350$ turns of wire, as shown in Fig. $9.1$.

May/June 2020

State Faraday’s law for electromagnetic induction.

May/June 2020

A wire coil lies in a uniform magnetic field with flux density $B$. Its diameter is $3.6\,\text{cm}$ and it has $350$ turns of wire, as shown in Fig. 9.1.

May/June 2020

State Lenz’s law in words.

May/June 2021

State what Lenz’s law says.

May/June 2021

What does magnetic flux mean?

May/June 2022

State Faraday’s law governing electromagnetic induction.

May/June 2022

Define the term magnetic flux.

May/June 2022

A substantial aluminium disc has radius $0.36\,\text{m}$. It turns together with the wheels of a vehicle and is part of an electromagnetic braking system on the vehicle. To switch on the braking system, a uniform magnetic field of flux density $0.17\,\text{T}$ is activated. This magnetic field is at right angles to the plane of rotation of the disc, as shown in Fig. 6.1.

May/June 2023

State Faraday’s law for electromagnetic induction.

May/June 2024

Fig. 6.1 shows a basic transformer fitted with an iron core.

Oct/Nov 2010

Fig. 6.1 shows a basic transformer with an iron core.

Oct/Nov 2010

As illustrated in Fig. 5.1, the two poles of a horseshoe magnet each have dimensions $5.0\text{ cm} \times 2.4\text{ cm}$. The magnetic flux density in the space between the poles is uniform at $89\text{ mT}$. In all regions outside the poles, the magnetic flux density is zero. A rigid copper wire is attached to a sensitive ammeter with resistance $0.12\,\Omega$. The wire is then pushed by a student at a steady speed of $1.8\text{ m s}^{-1}$ through the gap between the poles, moving parallel to the pole faces.

Oct/Nov 2010

State Lenz’s law in words.

Oct/Nov 2012

Wire pairs carrying telephone signals may experience cross-linking.

Oct/Nov 2012

State the principle known as Lenz’s law.

Oct/Nov 2012

State the connection between magnetic flux density $B$ and magnetic flux $\phi$, and define any other symbols you use.

Oct/Nov 2012

Fig. 5.1 shows an incomplete diagram of the magnetic flux pattern produced by a current-carrying solenoid.

Oct/Nov 2013

Fig. 5.1 shows an unfinished diagram of the magnetic flux pattern produced by a solenoid carrying current.

Oct/Nov 2013

A uniform magnetic field with flux density $B$ is inclined at an angle $\theta$ to the flat plane PQRS, as illustrated in Fig. 5.1. The area of plane PQRS is $A$.

Oct/Nov 2013

An output device is to be used to monitor the output potential $V_{\text{OUT}}$ from an operational amplifier. The output $V_{\text{OUT}}$ may be either $+5\,\text{V}$ or $-5\,\text{V}$.

Oct/Nov 2015

Suggest an explanation for each observation below.

Oct/Nov 2015

State Faraday’s law governing electromagnetic induction.

Oct/Nov 2016

State Faraday’s law for electromagnetic induction.

Oct/Nov 2016

State Faraday’s law for electromagnetic induction.

Oct/Nov 2016

State Faraday’s law for electromagnetic induction.

Oct/Nov 2018

A Hall probe is positioned close to one end of a solenoid wound around a soft-iron core, as illustrated in Fig. 9.1. The current in the solenoid is then turned on. The Hall probe is turned until the voltmeter reading $V_H$ reaches a maximum. The current in the solenoid is next changed, so that the magnetic flux density alters. The way the magnetic flux density $B$ at the Hall probe varies with time $t$ is shown in Fig. 9.2. At time $t = 0$, the Hall voltage is $V_0$.

Oct/Nov 2018

State Faraday’s law of electromagnetic induction.

Oct/Nov 2018

State Faraday’s law relating to electromagnetic induction.

Oct/Nov 2019

What is the definition of magnetic flux?

Oct/Nov 2020

A compact coil is set near one end of a solenoid that is connected to a power supply. The plane of the compact coil is perpendicular to the axis of the solenoid, as shown in Fig. 9.1. The power supply makes the current $I$ in the solenoid vary with time $t$ as shown in Fig. 9.2.

Oct/Nov 2020

Define magnetic flux by referring to the product of magnetic field strength and area.

Oct/Nov 2020

State, with reference to the power dissipated in a resistor, the meaning of the root-mean-square (r.m.s.) value of an alternating voltage.

Oct/Nov 2021

Fig. 10.1 illustrates a basic transformer with a laminated iron core, having a primary coil with 25 000 turns and a secondary coil with 625 turns. The output potential difference (p.d.) $V_{\text{OUT}}$ is connected across a load resistor of resistance $640\,\Omega$.

Oct/Nov 2021

State, by referring to the power dissipated in a resistor, what the root-mean-square (r.m.s.) value of an alternating voltage means.

Oct/Nov 2021

State Lenz’s law for electromagnetic induction.

Oct/Nov 2022

A metal wheel is made up of an axle A, eight spokes and a rim, as shown in Fig. 1.1. Point X lies on the rim at the outer end of one spoke. The rim has a radius of $0.85\,\text{m}$. The wheel is turning clockwise at an angular speed of $140\,\text{rad s}^{-1}$.

Oct/Nov 2024

An aircraft is travelling horizontally at a steady speed $v$ through the Earth’s magnetic field, as illustrated in Fig. 7.1. At the aircraft’s position, the vertical component of the Earth’s magnetic field is $38\,\mu\text{T}$ directed towards the ground. The separation between the wingtips P and Q of the aircraft is $68\,\text{m}$. While the aircraft passes through the magnetic field, an electromotive force (e.m.f.) of $0.54\,\text{V}$ is induced across the wingtips P and Q.

Oct/Nov 2025

An aircraft is travelling horizontally at a constant speed $v$ in the Earth’s magnetic field, as illustrated in Fig. 7.1. At the aircraft’s position, the vertical component of the Earth’s magnetic field is $38\,\mu\text{T}$ directed towards the ground. The separation between the wingtips P and Q of the aircraft is $68\,\text{m}$. As the aircraft passes through the field, an electromotive force (e.m.f.) of $0.54\,\text{V}$ is induced between the wingtips P and Q.

Oct/Nov 2025

A helicopter in steady hover has four rotors, each measuring $12\,\text{m}$ in length, as shown in the top view in Fig. 7.1. At the helicopter, the vertical part of Earth’s magnetic field points downwards and has a flux density of $0.047\,\text{mT}$. Each rotor turns in the horizontal plane in the direction indicated, with a frequency of $85\,\text{Hz}$.

Oct/Nov 2025