D.2 Electric and magnetic fields

Point charges of +2.0 μC and −3.0 μC are 0.10 m apart in a vacuum.

Which row gives the magnitude of the electric force between the charges and describes the force?

Two parallel plates 0.020 m apart are connected to a 240 V supply.

Which row gives the electric field strength between the plates and the magnitude of the force on an electron between them?

Two parallel metal plates carry equal and opposite charges.

Which statement about the electric field lines is correct?

Two identical small metal spheres X and Y on insulating stands carry charges of +6.0 nC and −2.0 nC. The spheres are touched together and then separated.

Which row gives the final charges on X and Y?

A hollow metal sphere carries a positive charge.

Which row describes the electric field inside the sphere and just outside it?

A plastic comb is pulled through dry hair. Afterwards the comb is negatively charged.

Which statement explains this?

Two parallel metal plates are connected to a power supply that keeps the potential difference between them constant. P is a point between the plates, well away from the edges.

Which change increases the electric field strength at P?

Inside a thundercloud, a raindrop carrying a charge of −3.2 pC is in an electric field of strength 5.0 × 10⁴ N C⁻¹ directed vertically upwards.

Which row gives the magnitude and the direction of the electric force on the raindrop?

In Millikan's experiment the electric charges on a large number of oil drops were determined.

Which statement describes what the results showed?

A student sprinkles iron filings on a sheet of card placed over a bar magnet and uses small plotting compasses to find the direction of the magnetic field.

Which statement about the magnetic field lines of the bar magnet is correct?

The main magnet of a hospital MRI scanner is a long solenoid carrying a large steady current. Which statement describes the magnetic field in the central region inside the solenoid?

A vertical copper earthing conductor on the side of a building carries a current directly upwards. Ignore the Earth's magnetic field. What is the direction of the magnetic field produced by the conductor at a point a short distance due east of it?

In electrostatic spray painting, a charged spray nozzle is held near a car body panel. The metal panel is connected to earth. Which statement about the electric field lines between the nozzle and the panel is correct?

A proton and an electron are each placed, one at a time, in the same uniform electric field inside a particle detector. Which statement is correct?

A high-voltage switch has two flat parallel electrodes separated by an air gap. The electric field strength in the gap is E. The engineer doubles both the potential difference across the electrodes and their separation. What is the new electric field strength in the gap?

In a vacuum tube, an electron is released from rest between two horizontal parallel plates. The upper plate is positive and the lower plate is negative. Gravitational effects are negligible. Which describes the motion of the electron before it reaches a plate?

Two parallel plates 4.0 cm apart have a potential difference of 500 V. An external agent moves a small charge of +2.0 μC slowly from the negative plate to the positive plate. What is the work done by the external agent on the charge?

Two large parallel plates produce a uniform field. Point X is close to the positive plate, point Y is midway between the plates and point Z is close to the negative plate. All three points are far from the plate edges. Which relationship between the field strengths at X, Y and Z is correct?

A child slides down an inflatable PVC play slide and, at the bottom, is found to be positively charged. The slide becomes negatively charged. Which statement explains this?

An uncharged metal sphere stands on an insulating base. The following steps are carried out in order:
1. A negatively charged rod is held close to the sphere, without touching it.
2. The sphere is briefly connected to earth.
3. The earth connection is removed.
4. The rod is taken away.
What is the final charge on the sphere?

A sensitive sensor is mounted inside a hollow spherical metal shell of radius R in a high-voltage laboratory. The shell carries a total charge +Q, and there are no other charges inside the shell. What is the electric field strength produced by this charge at the sensor, a distance R/2 from the centre?

Two small charged spheres in a dust-filter test rig are a distance r apart and exert an electric force of magnitude F on each other. The charge on each sphere is doubled and the separation is increased to 3r. What is the new magnitude of the force?

A vertical cable inside a lamp post carries a steady current directed vertically upwards. The magnetic field lines around the cable are viewed from directly above. Which describes them?

Which statement about electric field lines is correct?

A toner particle in a laser printer carries a net charge. Which of the following could be the magnitude of the charge on the particle?

A volleyball is rubbed against a synthetic court surface. It ends up with a charge of −8.0×10⁻⁹ C. Which statement describes the ball?

A nanoparticle charge detector records the following charges on four particles:
3.2×10⁻¹⁹ C, 4.8×10⁻¹⁹ C, 8.0×10⁻¹⁹ C, 11.2×10⁻¹⁹ C.
What is the largest value of a basic unit of charge that is consistent with all four readings?

A student claims that a charged speck of dust carries a charge of +1.0×10⁻¹⁹ C. Why is this claim impossible?

A student draws electric field lines to show the field around a charged dust particle inside an electrostatic air purifier. Which statement about electric field lines is correct?

In a laser-printer demonstration, two identical small conducting spheres carry charges of +6.0 nC and −2.0 nC. They are touched together and then separated. What is the charge on each sphere afterwards?

A footballer pulls a synthetic training shirt off over her head. The shirt gains a charge of −4.8 nC. Which statement is correct? (e = 1.60×10⁻¹⁹ C)

A small charge +q placed at point P experiences an electric force of magnitude F directed due east.

The charge is removed and replaced by a charge −2q. Which row gives the electric field strength at P and the force on the charge −2q?

Two small charged spheres in air exert an electric force F on each other. The permittivity of air is ε₀.

The spheres are immersed in an insulating liquid of permittivity 5.0ε₀, with the same charges and the same separation. What is the force between them now?

In a Millikan-type experiment the charges measured on three oil drops are 3.2 × 10⁻¹⁹ C, 6.4 × 10⁻¹⁹ C and 8.0 × 10⁻¹⁹ C.

What is the largest value of the elementary charge that is consistent with all three results?

Two point charges of equal magnitude are fixed a short distance apart, and M is the midpoint between them. Either charge on its own would produce an electric field of magnitude E at M.

Which row gives the magnitude of the resultant electric field at M when the charges are both positive and when they have opposite signs?

A long straight wire is perpendicular to the page and carries a current into the page (⊗).

Which diagram best shows the magnetic field lines around the wire in the plane of the page?

Two point charges exert a force of magnitude F on each other. Both charges are doubled and their separation is trebled.

What is the magnitude of the new force?

The north-seeking end of a compass needle points towards the Earth's geographic North Pole.

Which row describes the magnetic pole of the Earth that lies near its geographic North Pole and the direction of the Earth's magnetic field lines there?

In a Millikan-type experiment, two oil drops X and Y are each held stationary in turn between the same horizontal parallel plates by adjusting the potential difference V between the plates.

The drops are made of the same oil. Drop X has twice the radius of drop Y. X carries four electron charges and Y carries two. Buoyancy can be ignored.

What is V_X/V_Y?

Two uncharged metal spheres X and Y stand on insulating supports and touch each other. A negatively charged rod is held close to X, without touching it. With the rod still in place, Y is moved away from X. The rod is then removed.

Which row describes the final charges on X and Y?

The diagram shows a cross-section, in the plane of the page, through two long, straight, parallel wires X and Y that are perpendicular to the page. The wires carry equal currents, out of the page in X and into the page in Y. M is midway between them.

Either current alone produces a magnetic field of magnitude B at M.

Which row gives the magnitude and the direction of the resultant magnetic field at M?

A sensitive electronic instrument is placed inside a closed, uncharged metal box that stands on an insulating base. The box is then placed in a strong external electric field. The electric field inside the box is zero.

Which statement explains why the field inside the box is zero?

Two equal positive point charges are fixed at points P and R. X is a point on the straight line between P and R, at a distance x from P. E is the component of the resultant electric field at X in the direction from P towards R.

Which graph shows how E varies with x between P and R?

After a journey, friction with the air has left the metal body of a road tanker, which rests on insulating rubber tyres, with a positive charge of 4.8 μC. Before unloading, the driver connects the body to earth with a metal cable, and the body becomes uncharged.

Which row gives the number of electrons that pass through the cable and the direction in which they move?

Point charges of +2.0 nC and −2.0 nC are fixed in a vacuum at the corners A and B of an equilateral triangle ABC of side 0.30 m.

Which row gives the magnitude and the direction of the resultant electric field at C?

In Coulomb's law the constant k = 1/4πε₀, where ε₀ is the permittivity of free space.

What are the SI base units of ε₀?

A flat circular coil of wire lies in the plane of the page. The current I in the coil is clockwise as seen in the diagram. Point X is at the centre of the coil. Point Y is in the plane of the page, a short distance outside the coil.

Which row gives the direction of the magnetic field due to the current at X and at Y?

A proton and an alpha particle are released from rest a short distance apart in a vacuum. The charge of the alpha particle is 2e and its mass is 4 times the mass of the proton. Only the electric force acts.

Which row gives (magnitude of force on the proton)/(magnitude of force on the alpha particle) and (magnitude of acceleration of the proton)/(magnitude of acceleration of the alpha particle) when they are released?

Two large, parallel metal plates a small distance apart are connected to a power supply. Point X moves along the straight line through the centres of the plates, at right angles to them. It starts outside the plates, passes through the gap between them and ends outside the plates on the other side. The dashed lines in the sketch graphs show the positions of the positive and negative plates.

Which graph best shows how the magnitude E of the electric field strength at X varies with the position x of X?

Small test charges q, some positive and some negative, are placed in turn at point P near a fixed charged sphere S. The graph shows how the electric force F on the test charge varies with q. F is positive when it is directed away from S. The test charges do not disturb the charge on S.

Which row gives the electric field strength at P and the magnitude of the force on a +2.0 nC test charge at P after the charge on S has been doubled?

In a continuous inkjet printer, charged ink droplets pass between two parallel deflecting plates. The plates are 2.0 mm apart and have a potential difference of 1.5 kV across them. What is the magnitude of the electric field strength between the plates?

A dust grain above the lunar surface is modelled as a point charge. The electric field strength due to the grain is E at a distance r. The charge on the grain then doubles. What is the field strength due to the grain at a distance 3r?

In a test rig for an electrostatic air filter, two small spheres carry charges +4q and +q. Their centres are a distance d apart. At what distance from the +4q sphere, on the line between them, is the resultant electric field strength zero?

A domestic mains cable contains two long, parallel wires. At one instant they carry equal currents in opposite directions. At a distance x, one wire alone would produce a magnetic field of magnitude B. The point P is midway between the wires, a distance x from each. What is the magnitude of the resultant magnetic field at P?

In a test rig for electrostatic paint spraying, two small charged spheres are fixed a distance d apart. Sphere X carries charge +4Q and sphere Y carries charge +Q. At which point on the line between them is the resultant electric field zero?

A simple model of a polar molecule uses a charge +q and a charge −q separated by a distance 2a. What is the electric field at the midpoint between the charges?

In an electron-beam welding machine, electrons travelling horizontally enter the uniform vertical field between two horizontal deflecting plates. Gravitational effects are negligible. Which quantity stays constant while an electron is between the plates?

In an inkjet printer, a charged ink droplet has acceleration a while it passes between two deflecting plates. The potential difference across the plates is doubled and the plate separation is halved. The charge and mass of the droplet are unchanged. What is the new acceleration of the droplet?

A charged conducting sphere of radius R produces an electric field of strength E just outside its surface. What is the field strength at a point 2R from the surface of the sphere?

Two identical small conducting spheres carry charges of +6 nC and −2 nC. They attract each other with a force of magnitude F. The spheres are touched together and then returned to their original separation. What is the force between them now?

A hospital technician tests a plastic instrument tray for static charge. She uses a gold-leaf electroscope that has been given a positive charge. When the tray is brought near the cap, the leaves diverge further. What can be concluded about the tray?

A magnetic sensor in an electric-vehicle battery pack is a distance r from a long straight busbar and measures a field strength B. The current in the busbar is tripled and the sensor is moved to a distance r/2 from it. What field strength does the sensor now measure?

A two-core cable for a medical scanner consists of two long parallel conductors a distance d apart. Each carries current I, and the currents are in opposite directions. What is the magnitude of the magnetic field at the point midway between the conductors?

A sodium ion and a chloride ion are a fixed distance apart. When they are in vacuum, the electric force between them is F. The same pair is now placed at the same separation in water, which has a permittivity about 80 times that of vacuum. What is the force between them now?

In an ion-trap design, a point charge +4q is fixed at x = 0 and a point charge +q is fixed at x = d. At what position between them is the resultant electric force on a small test charge zero?

A hiker's compass is placed near a long vertical cable carrying a current of 10 A. The horizontal component of the Earth's magnetic field is 2.0 × 10⁻⁵ T. At what distance from the cable does the cable's field have the same magnitude as this component? (μ₀ = 4π × 10⁻⁷ T m A⁻¹)

Two protons in a particle-accelerator bunch are a distance d apart. The ratio of the electric force to the gravitational force between them is R. The separation is increased to 2d. What is the new ratio?

The electric force between two protons is far larger than the gravitational force between them. Yet gravity governs the motion of planets and moons. Which statement best explains this?

Two identical dust grains in deep space each carry the same charge q. The electric repulsion between them exactly balances their gravitational attraction. Two other identical grains each have twice the mass. What charge must each of these grains carry for the forces to balance?

In an evacuated tube, a uniform vertical electric field is adjusted until the electric force on a single electron exactly balances its weight. What is the electric field strength?
(m_e = 9.1×10⁻³¹ kg, e = 1.6×10⁻¹⁹ C, g = 9.8 m s⁻²)

A sensor contains two identical tiny conducting beads. One bead carries a charge of +5e and the other carries −2e. The beads touch and are then separated. Which is a possible final distribution of charge?

The metal skin of an aircraft becomes charged during flight. Once the charges have stopped moving, which describes the electric field lines just outside the aircraft's surface?

A field-line diagram shows two small charged spheres X and Y. Eighteen field lines leave X. Six of these lines end on Y, and the remaining twelve continue to very large distances. No lines leave Y. Which statement is correct?

Fluorine-18 (proton number 9) is used as a tracer in PET medical scanners. Which equation for its decay conserves electric charge?

In an industrial inkjet printer, a charged ink droplet passes through the central region between two parallel deflection plates held at a constant potential difference. Which statement about the electric force on the droplet in this region is correct?

An isolated positive point charge is modelled by a field-line diagram. At distance r from the charge, n field lines pass through a small area held perpendicular to the lines. How many lines pass through the same area at distance 2r?

Two parallel plates 0.050 m apart have a potential difference of 500 V between them. An electron is released from rest at the negative plate and accelerates to the positive plate.

Which row gives the kinetic energy of the electron when it reaches the positive plate?

A negatively charged rod is brought near one end of an isolated metal sphere on an insulating stand. The far side of the sphere is then briefly earthed, the earth connection is removed, and finally the rod is taken away.

What is the final charge on the sphere?

In a three-dimensional model of an electric field, neighbouring field lines in region P are twice as far apart as those in region Q, measured in every direction at right angles to the field.

What is (field strength in Q) : (field strength in P)?

A charged oil drop is held stationary between two horizontal parallel plates. The potential difference between the plates is then reversed, keeping the same magnitude. Ignore the buoyancy force of the air.

Which row gives the magnitude and the direction of the initial acceleration of the drop? g is the acceleration of free fall.

The diagram shows the electric field lines around two point charges X and Y. Twelve field lines leave X.

Which row gives the sign of the charge on X and the value of (magnitude of the charge on X)/(magnitude of the charge on Y)?

Which statement about electric field lines is correct?

The solenoid of an electric door lock is an air-core coil with ends P and Q. When the coil is viewed looking at end P, the current in the coil is clockwise. A small compass is placed inside the solenoid, on its axis.

Which row gives the magnetic pole at end P and the end towards which the north-seeking end of the compass needle points?

In a particle-steering device, one pair of plates produces a uniform vertical field of 3.0 kV m⁻¹. A second pair produces a uniform horizontal field of 4.0 kV m⁻¹ in the same region. An electron is released from rest in this region. Gravitational effects are negligible. Which describes the subsequent motion of the electron?

A small charge +q is held at the centre of an uncharged hollow metal sphere without touching it. The sphere is connected to earth, and then the connection is removed. The charge +q remains at the centre. What are the charges on the inner and outer surfaces of the metal sphere?

Two identical small conducting spheres in a static-electricity sensor carry charges of +6 nC and −2 nC. They attract each other with a force of magnitude F. The spheres are briefly touched together and then returned to their original separation. What is the new force between them?

Three identical conducting spheres are mounted on insulating stands. Sphere A carries +9.0 nC, sphere B carries −3.0 nC and sphere C is uncharged. A is touched to B and then separated. B is then touched to C and separated. What is the final charge on C?

A student investigates the charges produced when a polythene strip is rubbed with a woollen cloth. After rubbing, the strip and then the cloth are each lowered into a metal can (a Faraday pail) connected to a digital coulombmeter, which measures the charge on the object. The student holds the cloth in one hand and the strip by an insulating handle.

The procedure is repeated five times. Each charge reading has an uncertainty of ±0.4 nC.

A small conducting ball of mass 0.250 g hangs from an insulating thread of length 0.300 m midway between two vertical parallel plates separated by (120 ± 1) mm. The ball carries a fixed charge q. When a potential difference V is applied across the plates, the ball is pushed sideways and its horizontal displacement x is read from a millimetre scale behind it, with an uncertainty of ±1 mm. The uncertainty in V is ±0.1 kV.

For small displacements, the horizontal electric force on the ball is F = mgx/L, where L is the length of the thread.

Two square metal plates of side 0.10 m are held parallel and connected to a 2.00 kV supply. An electric field meter measures the field strength E at the point midway between the centres of the plates. The separation d of the plates is varied from 20 mm to 125 mm. The uncertainty in each value of E is ±0.5 kV m⁻¹.

The graph shows E against 1/d.

A student uses a compass to determine the horizontal component B_E of the Earth's magnetic field. A long straight horizontal wire runs from south to north and carries a steady current of (3.00 ± 0.02) A towards the north. A small compass rests on a horizontal card directly below the wire, at a distance r below the centre of the wire, and is deflected through an angle θ from north. The angle is read to ±1° and r is measured to ±1 mm.

At the compass, the magnetic field of the wire is horizontal and at right angles to B_E, so tan θ = B/B_E, where B = μ₀I/(2πr) is the flux density due to the wire and μ₀ = 4π × 10⁻⁷ T m A⁻¹.

A student investigates charging by friction. A motorised rig rubs a PTFE disc with a nylon brush, making n strokes. The disc is then lifted by an insulating handle and lowered into a metal cup connected to a digital coulombmeter, which measures the charge on the disc. The charge on the disc is negative; the table shows its magnitude Q. Before each trial the disc is wiped with a damp cloth and left to dry, to remove the charge from the previous trial.

The readings fluctuate slightly, and each value of Q has an uncertainty of ±0.3 nC. The graph shows the data with error bars.

A student investigates how the electric force between two charged spheres depends on their separation. A small conducting sphere on an insulating rod stands on an electronic balance of resolution 0.001 g. An identical sphere carrying charge of the same sign is clamped vertically above it. The repulsion increases the balance reading by Δm, so the electric force is F = (Δm)g.

The centre-to-centre separation r is varied. The student tests the hypothesis F ∝ rⁿ by plotting lg (Δm / g) against lg (r / m). Four of the points have been plotted.

A student uses a long air-core solenoid to determine the magnetic constant μ₀. The solenoid has 480 turns (counted) wound over a length of (0.240 ± 0.002) m. A magnetic field sensor placed at the centre of the solenoid, along its axis, measures the flux density B for different currents I. The uncertainty in each value of B is ±0.05 mT.

For a long solenoid, B = μ₀nI, where n is the number of turns per unit length.