Force on a moving charge

A particle carrying charge $+q$ and having mass $m$ moves through a vacuum at a steady speed of $1.6 \times 10^5\,\text{m s}^{-1}$. It enters a uniform magnetic field of flux density $9.7 \times 10^{-2}\,\text{T}$, as shown in Fig. 9.1. The magnetic field is perpendicular to the particle’s initial velocity and is also perpendicular to, and out of, the plane of the paper. A uniform electric field is applied in the same region as the magnetic field so that the particle travels through the fields without deviation.

Feb/March 2016

State what the term magnetic field means.

Feb/March 2017

As shown in Fig. 9.1, a thin slab of conducting material has faces PQRS and VWXY set at right angles to a uniform magnetic field of flux density $B$. Electrons enter the slab perpendicular to face SRXY. A potential difference, called the Hall voltage $V_H$, forms across two faces of the slab.

Feb/March 2018

An object moves in a circle at constant speed. State the names of two quantities that change as the motion continues.

Feb/March 2024

A velocity selector is made by combining an electric field with a magnetic field. Charged particles, known as ions, enter the space between parallel plates where the electric and magnetic fields are uniform, as shown in Fig. 6.1.

Feb/March 2025

A parallel beam of negatively-charged particles moves through a vacuum with speed $v$. They enter a region containing a uniform magnetic field with flux density $930\,\mu\text{T}$. At first, the particles move at right-angles to the magnetic field. Fig. 7.1 shows the path of one particle. In the magnetic field, the negatively-charged particles travel along a curved path with radius $7.9\,\text{cm}$. A uniform electric field is then introduced in the same region as the magnetic field. When the electric field strength is $12\,\text{kV m}^{-1}$, the particles pass through the region of fields without any deflection.

May/June 2010

State the meaning of a magnetic field.

May/June 2011

Explain how a uniform electric field together with a uniform magnetic field can be used to select the velocity of a charged particle. A diagram may be included if you wish.

May/June 2014

State which type or types of field may produce a force on an uncharged particle that is moving.

May/June 2015

State the type of field, or fields, that may produce a force on a particle that is uncharged and moving.

May/June 2015

A slender rectangular piece of aluminium measures $65\,\text{mm}$ by $50\,\text{mm}$ by $0.10\,\text{mm}$, as shown in Fig. 9.1. Several corners of the piece are marked. A current $I$ of $3.8\,\text{A}$ is perpendicular to face RSXY of the piece. In aluminium, the free-electron number density is $6.0 \times 10^{28}\,\text{m}^{-3}$. A uniform magnetic field of magnetic flux density $B$ of $0.13\,\text{T}$ is perpendicular to face QRYZ of the aluminium piece, directed from Q to P. A Hall voltage $V_{H}$ appears across the piece and is described by the expression $V_{H} = \frac{BI}{ntq}$.

May/June 2016

A magnetic field with flux density $B$ is perpendicular to face $PQRS$ of a slice made of conducting material, as Fig. 9.1 shows. A current $I$ in the slice is perpendicular to face $QRZY$ of the slice. The Hall voltage $V_H$ across the slice is given by $V_H = \dfrac{BI}{ntq}$.

May/June 2016

Fig. 9.1 shows a thin rectangular aluminium slice with side lengths of $65\,\text{mm}$, $50\,\text{mm}$ and $0.10\,\text{mm}$. Some corners on the slice are labelled. A current $I$ of $3.8\,\text{A}$ is directed normal to face RSXY of the slice. Aluminium contains $6.0 \times 10^{28}\,\text{m}^{-3}$ free electrons per unit volume. A uniform magnetic field with magnetic flux density $B$ of $0.13\,\text{T}$ is normal to face QRYZ of the aluminium slice and points from Q to P. A Hall voltage $V_{H}$ is produced across the slice and is described by $V_{H} = \frac{BI}{ntq}$.

May/June 2016

An electron with charge $-q$ and mass $m$ is accelerated from rest in a vacuum by a potential difference $V$. It then enters a region where the magnetic flux density is a uniform $B$, as shown in Fig. 7.1. The uniform magnetic field points into the plane of the paper. On entering the magnetic field, the velocity of the electron is normal to the magnetic field. The radius of the circular path followed by the electron in the magnetic field is $r$.

May/June 2017

As shown in Fig. 9.1, a Hall probe is positioned close to one end of a current-carrying solenoid. It is turned about the axis $XY$ and then kept in the orientation that gives the greatest Hall voltage.

May/June 2017

An electron with charge $-q$ and mass $m$ starts from rest in a vacuum and is accelerated through a potential difference $V$. It then moves into a region of uniform magnetic field of magnetic flux density $B$, as shown in Fig. 7.1. The uniform magnetic field is directed into the plane of the paper. The electron’s velocity on entry to the magnetic field is perpendicular to the field. The radius of the circular path of the electron in the magnetic field is $r$.

May/June 2017

Explain how a uniform magnetic field together with a uniform electric field can be used as a velocity selector for charged particles.

May/June 2018

An electron is moving through a vacuum at a speed of $3.4 \times 10^7\,\text{m s}^{-1}$. It then enters a region of uniform magnetic field with flux density $3.2\,$mT, as shown in Fig. 8.1. The electron initially travels at an angle of $30^\circ$ to the direction of the magnetic field.

May/June 2019

An electron moves in a vacuum in a straight line at speed $v$. It then enters a uniform magnetic field with flux density $8.0 \times 10^{-4}\,\text{T}$. At the instant it enters, the electron travels at right angles to the magnetic field, as shown in Fig. 9.1. Inside the magnetic field, the electron follows a circular arc of radius $6.4\,\text{cm}$.

May/June 2020

State what the term magnetic field means.

May/June 2021

Define magnetic flux density in terms of the force on a current-carrying conductor.

May/June 2021

State what the term magnetic field means.

May/June 2021

A sphere with mass $1.6 \times 10^{-10}\,\text{kg}$ carries a charge of $+0.27\,\text{nC}$. It lies in a uniform electric field acting vertically upwards, as illustrated by the side view in Fig. 2.1. The electric force on the sphere keeps it at one fixed vertical level in a horizontal plane. A uniform magnetic field is present in the same region as the electric field. The sphere travels at $0.78\,\text{m s}^{-1}$ in the horizontal plane. This magnetic field makes the sphere follow a circular path of radius $3.4\,\text{m}$, as shown in the view from above in Fig. 2.2.

May/June 2022

A sphere with mass $1.6 \times 10^{-10}\,\text{kg}$ carries a charge of $+0.27\,\text{nC}$. It is placed in a uniform electric field acting vertically upwards, as shown in the side view in Fig. 2.1. The force from the electric field keeps the sphere at a fixed vertical height in a horizontal plane. A uniform magnetic field is also present in the electric-field region. The sphere travels at a speed of $0.78\,\text{m s}^{-1}$ in the horizontal plane. This magnetic field makes the sphere follow a circular path of radius $3.4\,\text{m}$, as shown in the view from above in Fig. 2.2.

May/June 2022

Define the term electric field.

May/June 2024

Define what magnetic flux density is.

May/June 2025

Define magnetic flux density in terms of the force acting on a current‑carrying conductor in a magnetic field.

May/June 2025

A beam of positive ions passes through a vacuum in a fine stream. The ions then move into a region where the magnetic field has uniform flux density $B$, and they are bent into a semi-circular path, as shown in Fig. 5.1. These ions, moving at speed $1.40 \times 10^5\,\text{m s}^{-1}$, are recorded by a fixed detector when the arc formed in the magnetic field has a diameter of $12.8\,\text{cm}$.

Oct/Nov 2010

Positive ions move through a vacuum as a thin beam. They enter a region where the magnetic field has uniform flux density $B$ and are bent into a semi-circular path, as shown in Fig. 5.1. The ions, moving at speed $1.40 \times 10^{5}\,\text{m s}^{-1}$, are recorded by a fixed detector when the diameter of the arc in the magnetic field is $12.8\,\text{cm}$.

Oct/Nov 2010

Electrons travel in a vacuum as a narrow beam. They have speed $v$ and then enter a region where the magnetic field is uniform, with flux density $B$. At first, the electrons move at right angles to the magnetic field. The trajectory of one electron is shown in Fig. 7.1. In the magnetic field, the electrons take a curved route. A uniform electric field of field strength $E$ is then applied in the same region as the magnetic field. The electrons pass through the region without any deflection. Gravitational effects can be ignored.

Oct/Nov 2010

Positively charged particles move in a vacuum through three narrow slits $S_1$, $S_2$ and $S_3$, as illustrated in Fig. 5.1. Each particle travels at speed $v$ and carries charge $q$. A uniform magnetic field of flux density $B$ and a uniform electric field of field strength $E$ occupy the region between slits $S_2$ and $S_3$.

Oct/Nov 2011

Positively charged particles move through a vacuum, passing via three narrow slits $S_1$, $S_2$, and $S_3$, as illustrated in Fig. 5.1. Each particle travels with speed $v$ and carries charge $q$. In the space between slits $S_2$ and $S_3$, there is a uniform magnetic field of flux density $B$ together with a uniform electric field of field strength $E$.

Oct/Nov 2011

Define tesla.

Oct/Nov 2011

State the condition under which a charged particle experiences a force in a magnetic field.

Oct/Nov 2012

State the condition that allows a charged particle to experience a force in a magnetic field.

Oct/Nov 2012

A proton with mass $m$ and charge $+q$ moves in a vacuum along a straight path at speed $v$. It then enters a region where the magnetic flux density is uniform and has magnitude $B$, as shown in Fig. 4.1. The magnetic field is at right angles to the proton’s direction of travel.

Oct/Nov 2012

A particle of mass $m$ carrying charge $-q$ moves through a vacuum with speed $v$. It then enters a uniform magnetic field with flux density $B$. The angle between the particle’s initial direction of travel and the magnetic field direction is $90^\circ$.

Oct/Nov 2013

A particle with mass $m$ and charge $-q$ moves through a vacuum at constant speed $v$. It then enters a uniform magnetic field with flux density $B$. The angle at entry between the particle’s direction of travel and the magnetic-field direction is $90^\circ$.

Oct/Nov 2013

A particle of mass $m$ and charge $+q$ moves through a vacuum at speed $v$. Its initial motion is parallel to the plane of two horizontal charged metal plates, as shown in Fig. 6.1. The uniform electric field between the plates has magnitude $2.8 \times 10^{4}\,\text{V m}^{-1}$ and is zero outside the plates. The particle goes between the plates and then emerges beyond them, as illustrated in Fig. 6.1.

Oct/Nov 2013

State the meaning of quantisation of charge.

Oct/Nov 2014

A particle of mass $m$, charge $+q$ and speed $v$ is moving parallel to a uniform gravitational field of strength $g$. State the magnitude and direction, if any, of the force on the particle.

Oct/Nov 2015

A particle of mass $m$, charge $+q$ and speed $v$ is moving in the same direction as a uniform gravitational field of field strength $g$. State the magnitude and direction of any force acting on the particle.

Oct/Nov 2015

Explain what the term field of force means.

Oct/Nov 2016

Explain what is meant by a field of force.

Oct/Nov 2016

A narrow slab of conducting material is positioned at right angles to a uniform magnetic field of flux density $B$, as shown in Fig. 8.1. The magnetic field is at right angles to face CDEF and to face PQRS. A current $I$ flows through the slab and is at right angles to faces CDQP and FERS. A potential difference, the Hall voltage $V_H$, is produced across the slab.

Oct/Nov 2017

A thin conducting slice is set at right angles to a uniform magnetic field, as shown in Fig. 8.1. The magnetic field is normal to face $CDEF$ and to face $PQRS$. The current $I$ in the slice is normal to faces $CDQP$ and $FERS$. A potential difference, the Hall voltage $V_H$, develops across the slice.

Oct/Nov 2017

State what the term field of force means.

Oct/Nov 2017

A narrow conducting strip is positioned at right angles to a uniform magnetic field of flux density $B$, as shown in Fig. 8.1.

Oct/Nov 2017

Explain what a magnetic field means.

Oct/Nov 2018

Explain the meaning of a magnetic field.

Oct/Nov 2018

Electrons are incident at right angles to face PQFE of a rectangular semiconductor slice PQRSEFGH, as shown in Fig. 8.1. A uniform magnetic field with flux density $B$ is directed into the slice, at right angles to face PQRS.

Oct/Nov 2019

A conducting strip is shown in Fig. 8.1, with its face QRLK at right angles to a uniform magnetic field of flux density $B$. Electrons enter the strip moving at right angles to face PQKJ.

Oct/Nov 2020

A section of conducting material has face QRLK set perpendicular to a uniform magnetic field of flux density $B$, as shown in Fig. 8.1. Electrons move into the section in a direction perpendicular to face PQKJ.

Oct/Nov 2020

Fig. 6.1 depicts a thin semiconducting slice used in a Hall probe. Current $I$ flows through the slice in the direction indicated. The slice is set in a uniform magnetic field of flux density $B$, with two of its faces perpendicular to the magnetic field. A constant Hall voltage $V_H$ appears between face $PQXW$ and face $SRYZ$.

Oct/Nov 2022

Fig. 6.1 shows a narrow sheet of semiconducting material in a Hall probe. Current $I$ flows through the slice in the direction indicated. The slice is placed in a uniform magnetic field with flux density $B$, arranged so that two of its faces are at right angles to the magnetic field. A constant Hall voltage $V_H$ is produced between face $PQXW$ and face $SRYZ$.

Oct/Nov 2022

Define magnetic flux density.

Oct/Nov 2023

A Hall probe made from a thin slice of semiconducting material is inserted into a uniform magnetic field of flux density $B$. As shown in Fig. 7.1, the broad faces of the slice are at right angles to the magnetic field. The thickness $x$ of the slice is $1.8\,\text{mm}$. The number density of charge carriers in the semiconducting material is $1.5 \times 10^{16}\,\text{m}^{-3}$. A steady current of $5.4\,\text{A}$ is driven through the slice between the shaded faces. The Hall voltage $V_H$ developed across terminals $PQ$ is measured. Fig. 7.2 shows how $B$ varies with time $t$.

Oct/Nov 2023

Define the term magnetic flux density.

Oct/Nov 2023