Magnetic Fields (AQA A Level Physics)

Figure 1 shows a section of a horizontal copper wire carrying a current of 1.3 A.

A horizontal uniform magnetic field of flux density B is applied at right angles to the wire in the direction shown in the figure. 

Figure 1

State the direction of the magnetic force that acts on the moving electrons in the wire as a consequence of the current and explain how you arrive at your answer.

Copper contains 8.4 × 10²⁸ free electrons per cubic metre. The section of wire in Figure 1 is 125 mm long and has a cross-sectional area of 2.8 × 10^–5 m². 

Show that there are about 3 × 10²³ free electrons in this section of wire.

With a current of 1.3 A, the average velocity of an electron in the wire is 3.5 × 10^–6 m s^–1 and the average magnetic force on one electron is 1.8 × 10^–25 N.

Calculate the flux density B of the magnetic field.

The direction of the magnetic field changes such that the weight of the wire is supported by the magnetic force that acts upon it. 

Calculate the minimum value of the flux density of the magnetic field in which the wire should be placed.

Density of copper = 8.9 × 10³ kg m^–3

The diagram above shows a double-charged positive ion of the iron isotope    that is projected into a vertical magnetic field of flux density 0.18 T, with the field directed upwards. 

Figure 1

The ion enters the field at a speed of 5.9 × 10⁵ m s^–1. 

State the initial direction of the magnetic force that acts on the ion.

Describe the subsequent path of the ion.Your answer should include both a qualitative description and a calculation. 

Mass of   ion = 9.33 × 10^–26 kg

Calculate the time taken for a double-charged iron ion to complete one orbit.

State the effect on the radius in Figure 1 and the time taken to complete an orbit if the following changes are made separately: 

(i) The strength of the magnetic field is doubled. 

(ii) A triple-charged positive  ion replaces the original one.

Cyclotrons are used to accelerate particles, such as protons, for a number of applications. 

A cyclotron has two D-shaped regions called ‘dees’ where the magnetic flux density is constant.The dees are separated by a small gap.An alternating electric field between the dees accelerates charged particles. The magnetic field causes the charged particles to follow a circular path. 

Figure 1 shows the path followed by a proton that starts from O.

 Figure 1

State and explain:

(i) Why it is not possible for the magnetic field to alter the speed of a proton while it is in one of the dees.

(ii) The direction in which the magnetic field should be applied in order for the protons to travel along the semi-circular paths inside each of the dees.

Show that the time taken by a proton to travel around one semi-circular path is independent of the radius of the path.

The maximum radius of the path followed by the proton is 0.46 m and the magnetic flux density of the uniform field is 0.88 T. 

Calculate the maximum speed of a proton when it leaves the cyclotron. 

Ignore any relativistic effects.

The protons leave the cyclotron when the radius of their path is equal to the outer radius of the dees. 

Ignoring any relativistic effects, calculate the radius required for the cyclotron to produce:

(i) Protons with a maximum kinetic energy of 25 MeV. 

(ii) Protons which travel at half the speed of light.

Discuss two situations in which a charged particle will experience no magnetic force when placed in a magnetic field.

Figure 1 shows an electron moving through a magnetic field. 

Figure 1

The magnetic field has a flux density of 0.38 T. The electron travels at a speed of 1.2 × 10⁷ m s^–1. 

(i) Draw the direction of the force acting on the electron due to the magnetic 

(ii) Calculate the size of the electron’s acceleration.

An electron is fired into a chamber containing a magnetic field as shown in Figure 2.  

Figure 2

The chamber is 60 mm wide and the magnetic field is perpendicular to the plane containing the moving electron. The electron has 6.30 × 10^-16 J of kinetic energy.

Calculate the strength of the magnetic field if the electron is to just miss colliding with the opposite plate.

A section of a straight current-carrying wire is placed at right angles to a uniform magnetic field of flux density B. When the current in the wire is I, the magnetic force that acts on this section is F. 

A second section of wire is placed at right angles to a uniform magnetic field of flux density 4B when the current is 0.75 I. 

Calculate the force that acts on the second wire.

The first wire is placed in a uniform magnetic field of flux density B, with current I, and magnetic force F. The uniform magnetic field covers 90 mm of the wire. 

The same length of the second wire is placed in a west-east direction as shown in Figure 1.

Figure 1

The magnetic flux density of the second wire is 80 mT and is directed downwards into the plane of the diagram. When a current of 3.0 A passes through the second wire from west to east, a force acts on it. 

Calculate the magnitude and direction of the force on the first wire.

One of the wires is bent into a square coil. 

The coil is mounted on an axle O and is placed with its plane parallel to the flux lines of a uniform magnetic field B, as shown in Figure 2. 

Figure 2

Then, the coil is then placed at right angles to the magnetic field as shown in Figure 3. 

Figure 3

The current, I, is switched on and flows through sides PQRS. 

Before the coil is allowed to move, describe the forces on sides SP and QR in: 

(i) Figure 2. 

(ii) Figure 3.

The wire is then bent into a circular coil, as shown in Figure 4. 

The circular coil is placed in a uniform magnetic field B with the plane of the coil perpendicular to the magnetic field. 

Figure 4

The current, I, is switched on and flows in a clockwise direction. 

Describe the effect on the coil from the interaction between the current and the magnetic field.

A mass spectrometer is an instrument used to analyse the atoms present in a sample of gas. The atoms are ionised in order to produce positive ions and then passed through a velocity selector, as shown in Figure 1.

Figure 1

The velocity selector consists of electric and magnetic fields acting at right angles to each other.

The magnetic field is directed into the page. The electric field is produced by a pair of parallel plates of separation d with a high potential difference, V, across them.

Discuss how the velocity of an ion affects the path it takes through the velocity selector.

The magnetic field strength is 260 mT, the potential difference across the plates is 1200 V and the plate separation is 2 cm.

Calculate the velocity of each ion passing straight through the selector.

A mixture of singly-ionised lithium isotopes of mass 6u and 7u leave the velocity selector with a velocity of 4.8 × 10⁴ m s^-1.

The ions enter a uniform magnetic field which exerts a force on them causing them to strike the detector. The upper edge of the detector is 40 mm from the point at which the charged ions enter the field, as shown in Figure 2.

Figure 2

Calculate the maximum magnetic field strength that can be applied in order for both ions to be detected.

A wire is held in tension between two fixed points, X and Y. A short section of the wire is positioned between the pole pieces of a permanent magnet, which applies a uniform horizontal magnetic field at right angles to the wire, as shown in Figure 1. 

Figure 1

Explain why the wire will vibrate vertically when an alternating electric current is passed through the wire.

The length of XY is 0.40 m. When the wire is vibrating, transverse waves are propagated along the wire at a speed of 32 m s^–1.

Explain why the wire is set into large amplitude vibration in the first harmonic mode when the frequency of the a.c supply is 40 Hz.

A magnetic field of flux density 240 mT is produced by the permanent magnet and acts over a 60 mm length of the wire.

Calculate the maximum force on the wire when there is an alternating current of rms value 2.8 A through it.

An electron passes between two adjacent chambers. Each chamber contains a separate, uniform magnetic field.

The horizontal displacement of the electron after passing through the chambers is 90 mm, as shown in Figure 1. 

Figure 1

The magnetic field strength in the first chamber is 1.5 mT and the magnetic field strength in the second chamber is double that of the first chamber. The electron enters the first chamber perpendicular to the top surface and leaves the second chamber perpendicular to the bottom surface.

Calculate the velocity at which the electron enters the first chamber.

A cyclotron is a particle accelerator which consists of two D-shaped electrodes, called ‘dees’, enclosed in an evacuated chamber, as shown in Figure 2.

A high frequency, alternating square-wave potential difference, of amplitude , is applied between the gap of the dees.  When a charged particle crosses the gap between the dees the polarity reverses causing the particle to be accelerated by the potential difference between the dees.  

Figure 2

Under a magnetic field of 0.500 T and a square-wave potential difference of amplitude 340 V, particles of mass 6.64 × 10^-27 kg and charge +3.20 × 10^-19 C leave the cyclotron at Y where the radius is 0.750 m. 

Calculate the number of revolutions a charged particle undergoes before exiting the cyclotron.

Determine the frequency needed for the charged particle to be accelerated each time it crosses from one dee to the other.

Two square, parallel metal sheets are separated by 25 mm in a vacuum, the lower plate being earthed. A narrow beam of electrons enters symmetrically between the plates as shown in Figure 1. There is a uniform magnetic field of flux density 0.020 T, which is perpendicular to the beam and parallel to the plates, acting in the direction shown in Figure 1.  When a potential difference of 1500 V is applied to the plates, the electron beam is undeflected.  

Figure 1

Calculate the speed of the electron, assuming that the electric field between the plates is uniform.

The potential difference between the plates in Figure 1 can be adjusted. The electrons in the beam are travelling at a speed of 2.35 × 10⁵ m s^-1 when they enter just underneath the top plate in the same direction as before.

If the length of the side of each square plate is 5 cm, calculate the maximum potential difference between the plates which would cause the electron beam to just leave the plates at the opposite side to which it entered without touching the lower plate.

Assume that the electric and magnetic fields only act between the plates

The northern lights are a phenomenon where the sky glows green due to charged particles from the Sun becoming trapped in the Earth’s magnetic fields near the north pole. 

Some charged particles travel in a circle of radius 50 km in a region where the magnetic flux density is 6.0 × 10^-3 T.

Show that the charged particles causing the northern lights cannot be electrons.