A horizontal copper wire of mass 4.0 × 10⁻³ kg and length 80 mm is placed perpendicular to a horizontal magnetic field of flux density 0.16 T. The magnetic force acting on the wire supports the weight of the wire.

How many electrons are passing a point in the wire in each second?

A horizontal straight wire of length 0.30 m carries a current of 2.0 A perpendicular to a horizontal uniform magnetic field of flux density 5.0 × 10^–2 T. The wire ‘floats’ in equilibrium in the field.

What is the mass of the wire?

The diagram shows a horizontal conductor of length 50 mm carrying a current of 3.0 A at right angles to a uniform horizontal magnetic field of flux density 0.50 T.

What is the magnitude and direction of the magnetic force on the conductor ?

The diagram shows a rigidly-clamped straight horizontal current-carrying wire held mid-way between the poles of a magnet on a top-pan balance. The wire is perpendicular to the magnetic field direction.

The balance, which was zeroed before the switch was closed, read 161 g after the switch was closed. When the current is reversed and doubled, what would be the new reading on the balance?

Four rectangular loops of wire A, B, C and D are each placed in a uniform magnetic field of the same flux density B. The direction of the magnetic field is parallel to the plane of the loops as shown.

When a current of 1 A is passed through each of the loops, magnetic forces act on them. The lengths of the sides of the loops are as shown. Which loop experiences the largest couple?

The diagram shows a vertical square coil whose plane is at right angles to a horizontal uniform magnetic field B. A current, I, is passed through the coil, which is free to rotate about a vertical axis OO'.

Which one of the following statements is correct?

A horizontal straight wire of length 40 mm is in an east-west direction as shown in the diagram. A uniform magnetic field of flux density 50 mT is directed downwards into the plane of the diagram. When a current of 5.0 A passes through the wire from west to east, a horizontal force acts on the wire. Which line, A to D, in the table gives the magnitude and direction of this force?

A section of 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.

What force acts when the same section of wire is placed at right angles to a uniform magnetic field of flux density 2B when the current is 0.25 I?

A horizontal straight wire of length 0.30 m carries a current of 2.0 A perpendicular to a horizontal uniform magnetic field of flux density 5.0 × 10^–2 T. The wire ‘floats’ in equilibrium in the field.

What is the mass of the wire?

The diagram shows a rigidly-clamped straight horizontal current-carrying wire held mid-way between the poles of a magnet on a top pan balance. The wire is perpendicular to the magnetic field direction.

The balance, which was zeroed before the switch was closed, reads 112 g after the switch is closed. If the current is reversed and doubled, what will be the new reading on the balance?

Which one of the following could not be used as a unit of force?

A coil, mounted on an axle, has its plane parallel to the flux lines of a uniform magnetic field B, as shown. When a current I is switched on, and before the coil is allowed to move,

A wire lies perpendicularly across a horizontal uniform magnetic field of flux density 20 × 10⁻³ T so that 0.30 m of the wire is effectively subjected to the field. If the force exerted on this length of wire due to a current in it is 30 × 10⁻³ N downward, what is the current in the wire?

Which line, A to D, gives correct units for both magnetic flux and magnetic flux density?

The diagram shows a wire carrying a current, I, in the plane of the paper and in the south direction. A magnetic field is applied perpendicularly to the paper and acts into the paper. What is the direction of the force acting on the wire?

Different magnetic fields are present in the two chambers shown. A particle enters the first chamber at a velocity of 80 m s^–1 and is deflected into a circular path of radius 200 mm.

In the second chamber it follows a circular path of radius 100 mm

The particle leaves the second chamber at a speed of

Two charged particles, P₁ and P₂, follow circular paths as they move at right angles to the same uniform magnetic field. Both particles are travelling at the same speed.

The radius of the path travelled by P₁ is twice the radius of the path travelled by P₂.

The mass of P₁ is m and its charge is q.

What is the mass of P₂ and the charge of P₂?

Charged particles, each of mass m and charge Q, travel at a constant speed in a circle of radius r in a uniform magnetic field of flux density B.

Which expression gives the frequency of rotation of a particle in the beam?

Which one of the following statements is correct?

An electron follows a circular path when it is moving at right angles to

Two electrons, X and Y, travel at right angles to a uniform magnetic field. X experiences a magnetic force, FX, and Y experiences a magnetic force, FY.

What is the ratio shown if the kinetic energy of X is half that of Y?

The path followed by an electron of momentum p, carrying charge –e, which enters a magnetic field at right angles, is a circular arc of radius r.

What would be the radius of the circular arc followed by an α particle of momentum 2p, carrying charge +2e, which entered the same field at right angles?

Which line, A to D, in the table correctly describes the trajectory of charged particles which enter separately, at right angles, a uniform electric field, and a uniform magnetic field?

A beam of positive ions enters a region of uniform magnetic field, causing the beam to change direction as shown in the diagram.

What is the direction of the magnetic field?

When a β particle moves at right angles through a uniform magnetic field it experiences a force F. An α particle moves at right angles through a magnetic field of twice the magnetic flux density with velocity one tenth the velocity of the β particle. What is the magnitude of the force on the α particle?

Charged particles, each of mass m and charge Q, travel at a constant speed in a circle of radius r in a uniform magnetic field of flux density B. Which expression gives the frequency of rotation of a particle in the beam?

Two charged particles, P and Q, move in circular orbits in a magnetic field of uniform flux density. The particles have the same charge but the mass of P is less than the mass of Q. T_P is the time taken for particle P to complete one orbit and T_Q the time for particle Q to complete one orbit. Which one of the following is correct?

A negatively charged particle moves at right angles to a uniform magnetic field. The magnetic force on the particle acts

An electron moving with a constant speed enters a uniform magnetic field in a direction perpendicular to the magnetic field. What is the shape of the path that the electron would follow?

An electron moving with a constant speed enters a uniform magnetic field in a direction at right angles to the field. What is the subsequent path of the electron?

A jet of air carrying positively charged particles is directed horizontally between the poles of a strong magnet, as shown in the diagram.

In which direction are the charged particles deflected?

An electron moves due North in a horizontal plane with uniform speed. It enters a uniform magnetic field directed due South in the same plane. Which one of the following statements concerning the motion of the electron in the magnetic field is correct?

Particles of mass m, each carrying charge Q and travelling with speed v, enter a magnetic field of flux density B at right angles. Which one of the following changes would produce an increase in the radius of the path of the particles?

Particles of mass m carrying a charge Q travel in a circular path of radius r in a magnetic field of flux density B with a speed v. How many of the following quantities, if changed one at a time, would change the radius of the path?

• m

• Q

• B

• v

Protons, each of mass m and charge e, follow a circular path when travelling perpendicular to a magnetic field of uniform flux density B. What is the time taken for one complete orbit?

The path followed by an electron of momentum p, carrying charge −e, which enters a magnetic field at right angles, is a circular arc of radius r.

What would be the radius of the circular arc followed by an α particle of momentum 2p, carrying charge +2e, which entered the same field at right angles?

Which line, A to D, correctly describes the trajectory of charged particles which enter, at right angles, (a) a uniform electric field, and (b) a uniform magnetic field?

An α particle and a β^– particle both enter the same uniform magnetic field, which is perpendicular to their direction of motion. If the β^– particle has a speed 15 times that of the α particle, what is the value of the ratio

An electron moves due North in a horizontal plane with uniform speed. It enters a uniform magnetic field directed due South in the same plane. Which one of the following statements concerning the motion of the electron in the magnetic field is correct?

An electron moves into a region of uniform magnetic flux density between the poles of a magnet as shown in the diagram. The deflection of the electron will be

An alpha particle moves at one-tenth the velocity of a beta particle. They both move through the same uniform magnetic field at right angles to their motion. The magnitude of the ratio shown is

A rectangular coil of area A has N turns of wire. The coil is in a uniform magnetic field of flux density B with its plane parallel to the field lines. The coil is then rotated through an angle of 30° about axis PQ. What are the correct initial value and correct final value of the magnetic flux linkage?

The diagram shows a coil placed in a uniform magnetic field. In the position shown, the angle between the normal to the plane of the coil and the magnetic field is π/3 rad.

A rectangular coil of area A has N turns of wire. The coil is in a uniform magnetic field, as shown in the diagram.

When the coil is rotated at a constant frequency f about its axis XY, an alternating emf of peak value ε₀ is induced in it.

What is the maximum value of the magnetic flux linkage through the coil?

The graph shows how the magnetic flux, Φ, passing through a coil changes with time, t.

Which one of the following graphs could show how the magnitude of the emf, V, induced in the coil varies with t?

A 500 turn coil of cross-sectional area 4.0 × 10^–3 m² is placed with its plane perpendicular to a magnetic field of flux density 7.5 × 10^–4 T. What is the value of the flux linkage for this coil?

A bar magnet is pushed into a coil connected to a sensitive ammeter, as shown in the diagram, until it comes to rest inside the coil.

Why does the ammeter briefly show a non-zero reading?

A coil of 50 turns has a cross-sectional area of 4.2 × 10^–3 m². It is placed at an angle to a uniform magnetic field of flux density 2.8 × 10^–2 T, as shown in the diagram, so that angle θ = 50°.

What is the change in flux linkage when the coil is rotated anticlockwise until θ = 0°?

An aircraft, of wing span 60 m, flies horizontally at a speed of 150 m s^–1. If the vertical component of the Earth’s magnetic field in the region of the plane is 1.0 × 10^–5 T, what is the magnitude of the magnetic flux cut by the wings in 10 s?

The graph shows how the magnetic flux passing through a loop of wire changes with time. What feature of the graph represents the magnitude of the emf induced in the coil?

The magnetic flux through a coil of N turns is increased uniformly from zero to a maximum value in a time t. An emf, E, is induced across the coil. What is the maximum value of the magnetic flux through the coil?

Which line, A to D, gives correct units for both magnetic flux and magnetic flux density?

A coil P is connected to a cell and a switch.

A second closed coil Q is parallel to P and is arranged on the same axis.

When the switch is closed, coil Q experiences a force.

Which row describes the force on Q?

Three identical magnets P, Q and R are released simultaneously from rest and fall to the ground from the same height.

P falls directly to the ground.

Q falls through the centre of a thick horizontal conducting ring.

R falls through a similar ring that has a gap cut into it.

In which order do the magnets reach the ground?

A coil with 20 circular turns each of diameter 60 mm is placed in a uniform magnetic field of flux density 90 mT.

Initially the plane of the coil is perpendicular to the magnetic field lines as shown in Figure X.

The coil is rotated about a vertical axis by 90° in a time of 0.20 s so that its plane becomes parallel to the field lines as shown in Figure Y.

Assume that the rate of change of flux linkage remains constant.

What is the emf induced in the coil?

A vertical conducting rod of length l is moved at a constant velocity v through a uniform horizontal magnetic field of flux density B.

Which of the rows gives a correct expression for the induced emf between the ends of the rod for the stated direction of the motion of the rod?

The graph shows how the flux linkage, NΦ, through a coil changes when the coil is moved into a magnetic field.

The emf induced in the coil

A train is travelling at 20 m s^–1 along a horizontal track through a uniform magnetic field of flux density 4.0 × 10^–5 T acting vertically downwards.

What is the emf induced between the ends of an axle 1.5 m long?

In which one of the following applications does electromagnetic induction not take place?

When a magnet is dropped through an aluminium ring an emf is induced. A data logger connected to the ring records the variation of the induced emf ε with time t as shown below.

In a second experiment, the magnet is dropped from a greater height.

Which one of the following graphs best represents the induced emf in the second experiment?

A vertical conducting rod of length l is moved at a constant velocity v through a uniform horizontal magnetic field of flux density B.

Which line, A to D, in the table gives a correct expression for the induced emf for the stated direction of the motion of the rod?

A transformer, which is not perfectly efficient, is connected to a 230 V rms mains supply and is used to operate a 12 V rms, 60 W lamp at normal brightness. The secondary coil of the transformer has 24 turns.

Which line, A to D, in the table is correct?

A rectangular coil is rotated in a uniform magnetic field.

When the coil is rotated at a constant rate, an alternating emf ε is induced in it. The variation of emf ε, in volts, with time t, in seconds, is given by

ε = 20 sin (100 πt)

Which line, A to D, in the table gives the peak value ε₀ and the frequency f of the induced emf?

The magnetic flux through a coil of 5 turns changes uniformly from 15 × 10⁻³ Wb to 7.0 × 10⁻³ Wb in 0.50 s. What is the magnitude of the emf induced in the coil due to this change in flux?

Three vertical tubes, made from copper, lead and rubber respectively, have identical dimensions. Identical, strong, cylindrical magnets P, Q and R are released simultaneously from the same distance above each tube. Because of electromagnetic effects, the magnets emerge from the bottom of the tubes at different times.

resistivity of copper = 1.7 × 10^–8 Ωm

resistivity of lead = 22 × 10^–8 Ωm

resistivity of rubber = 50 × 1013 Ωm

The graph shows how the magnetic flux, Φ, passing through a coil changes with time, t.

Which one of the following graphs could show how the magnitude of the emf, V, induced in the coil varies with t?

Using the circuit shown, and with the switch closed, a small current was passed through the coil X. The current was slowly increased using the variable resistor. The current reached a maximum value and was then switched off.

The maximum reading on the microammeter occurred when

When a mobile phone is being recharged, the charger heats up. The efficiency of the transformer in the charger can be as low as 15% when drawing a current of 50 mA from a 230 V mains supply. If the charging current required is 350 mA, what is the approximate output voltage at this efficiency?

The output electromotive force (emf) of a simple ac generator can be increased by any of the four factors listed.

Which one of these factors should not be changed if the frequency of the output is to remain unaffected when the emf is increased?

The graph shows how the flux linkage, N, through a coil changes when the coil is moved into a magnetic field.

The emf induced in the coil

A bar magnet is pushed into a coil connected to a sensitive ammeter, as shown in the diagram, until it comes to rest inside the coil.

Why does the ammeter briefly show a non-zero reading?

The above graph shows how the output emf, ε, varies with time, t, for a coil rotating at angular speed ω in a uniform magnetic field of flux density B. Which one of the following graphs shows how ε varies with t when the same coil is rotated at angular speed 2ω in a uniform magnetic field of flux density 0.5 B?

The graph shows how the magnetic flux passing through a loop of wire changes with time.

A coil rotating in a magnetic field produces the following voltage waveform when connected to an oscilloscope.

With the same oscilloscope settings, which one of the following voltage waveforms would be produced if the coil were rotated at twice the original speed?

The magnetic flux through a coil of N turns is increased uniformly from zero to a maximum value in a time t. An emf, E, is induced across the coil.

What is the maximum value of the magnetic flux through the coil?

An aircraft, of wing span 60 m, flies horizontally at a speed of 150 m s^–1, If the vertical component of the Earth’s magnetic field in the region of the plane is 1.0 × 10^–5 T, what emf is induced across the wing tips of the plane?

The diagram shows a square coil with its plane parallel to a uniform magnetic field. Which one of the following would induce an emf in the coil?

The magnetic flux threading a coil of 100 turns drops from 5 × 10^–3 Wb to zero in 0.1 s. The average induced e.m.f., in V, is

A rectangular conducting loop is pulled horizontally through the gap between two vertical magnets as shown in the diagram.

Which one of the graphs best represents the variation of loop current I with time t as the loop moves at a constant speed from JKLM to J'K'L'M'?

The diagram below shows the waveform obtained when the output of an alternator is connected to a cathode ray oscilloscope.

Which one of the following best represents the output when the speed of rotation of the generator is doubled and no adjustment is made to the oscilloscope?

The mean power dissipated in a resistor is 47.5 μW when the root mean square (rms) voltage across the resistor is 150 mV.

What is the peak current in the resistor?

A transformer has 1150 turns on the primary coil and 500 turns on the secondary coil.

The primary coil draws a current of 0.26 A from a 230 V ac supply. The current in the secondary coil is 0.50 A. What is the efficiency of the transformer?

The above graph shows how the output emf, ε, varies with time, t, for a coil rotating at angular speed ω in a uniform magnetic field of flux density B. Which one of the following graphs shows how ε varies with t when the same coil is rotated at angular speed 2ω in a uniform magnetic field of flux density 0.5 B?

A coil rotating in a magnetic field produces the following voltage waveform when connected to an oscilloscope.

With the same oscilloscope settings, which one of the following voltage waveforms would be produced if the coil were rotated at twice the original speed?

The diagram below shows the waveform obtained when the output of an alternator is connected to a cathode ray oscilloscope.

Which one of the following best represents the output when the speed of rotation of the generator is doubled and no adjustment is made to the oscilloscope?