Electric fields & field strength

Questions 6 and 7 refer to the information below.

A high-voltage d.c. power supply was connected to two parallel metal plates and an ammeter, as shown.

6 The distance between the two plates was decreased.

Which row of the table is correct?

Flowers can attract bees by being colourful or by producing a scent. Some flowers also attract bees by producing an electric field.

When a bee gets close to a flower it can detect the electric field. The charge on the flower acts as a point charge at the centre of the flower.

At a distance of 0.06 m from the centre of a particular flower the potential is –16 V.

Show that the charge on this flower is about –0.1 nC.

The minimum field strength that a bee can detect is 120 V m^–1.

A teacher suggests that bees can detect the field when they are closer than 10 cm from the flower in (b)(i).

Deduce whether this suggestion is correct.

It is suggested that the hairs on a bee deflect slightly when close to the flower.

Explain what would cause a hair to deflect in an electric field.

At the Facility for Rare Isotope Beams (FRIB) isotopes of elements that do not occur naturally can be produced.

FRIB contains a linear accelerator. The initial section of the accelerator is shown.

Explain why the tubes get progressively longer.

A uranium atom (²³⁸₉₂U) has 80 electrons removed. The uranium ion is then accelerated between two adjacent tubes until its kinetic energy is 200 MeV per nucleon.

Calculate the accelerating potential difference.

Show that the uranium ions will reach a velocity of about 65% of the speed of light.

When a uranium ion hits a target at this speed the ion is likely to break up and produce smaller elements. One particular isotope produced in this way is⁴⁰₁₂Mg. The naturally occurring common stable isotope of magnesium is²⁴₁₂Mg. Explain why the break-up of²³⁸₉₂U is likely to produce unusual isotopes such as⁴⁰₁₂Mg.

Which of the following could not be accelerated in a LINAC?

A teacher demonstrates the electric field produced between two parallel metal plates. The plates are connected to a variable power supply, as shown. The power supply has a very large internal resistance and includes a voltmeter that indicates its output.

Add to the diagram to show the electric field between the two plates.

Explain why the reading on the voltmeter indicates the e.m.f. of the power supply.

The power supply output is increased until sparks are heard and are seen in the gap between the plates. Sparks form in air when the electric field strength exceeds 3.010⁶V m⁻¹ and the air becomes conducting for a short time.

Calculate the minimum potential difference across the plates for sparks to be created.

distance between parallel plates = 2.0 mm

Explain why the voltmeter reading decreases significantly whenever sparks are produced.

Overhead electricity cables for railway lines are supported by structures like the one shown.

An electric cable of mass 45 kg is suspended from a support rod X. A second support rod Y is attached to X. X and Y are attached at one end to a column.

The masses of support rods X and Y are negligible.

Determine, by taking moments, the force exerted on rod X by rod Y.

Complete the free‑body force diagram for support rod X.

A website gives a value of the electric field strength E, at two distances from the

Deduce whether these data are consistent with an inverse square law.

A student investigated the behaviour of small, positively charged oil drops in an electric field.

He introduced an oil drop between two horizontal metal plates. A potential difference V was applied to bring the oil drop to rest as shown.

Add to the diagram to show the polarity of the power supply when the oil drop is at rest.

The oil drop was at rest when V = 4870 V.

The student expected the charge on the oil drop to be a whole number multiple of the charge on an electron.

Deduce whether this is confirmed by the experimental data.

distance between top plate and bottom plate = 1.55 cm

The student determined the terminal velocity of the oil drop in order to obtain a value for the weight of the oil drop.

He disconnected the power supply and the oil drop fell downwards. He viewed the oil drop through a microscope.

Explain why the student should wait a short while before starting to take measurements.

The view through the microscope is shown below. The scale is in millimetres.

The position of the oil drop at the start and end of a 120 s time interval is indicated by the black dots.

Determine the terminal velocity of the oil drop.

The student repeated the measurements on fifty oil drops. For each drop the student calculated the charge on the oil drop.

His results are shown in the bar chart.

The student predicted that the charge on each oil drop would be a whole number multiple of the charge on an electron.

Comment on the extent to which the bar chart supports the student’s prediction.

A point object has a charge +Q.

Which of the following diagrams shows equipotential lines differing by a constant potential difference, and electric field lines around the object?

A series of experiments was carried out in the 1970s to investigate the structure of protons using the linac at Stanford, USA.

*(a) Explain how an electron is accelerated in a linac.

The electron leaves the accelerator with a high energy.

Explain why electrons need high energies to investigate the structure of a proton.

An electron leaves the accelerator with a momentum of 20 GeV / c.

Explain, with reference to base units, why GeV / c can be used as a unit of momentum.

An electron with initial momentum 20 GeV / c collides with a stationary proton. After the collision the electron is deflected by an angle of 20° as shown and its momentum is 9.1 GeV / c. The momentum of the proton after the collision is 11.9 GeV / c.

Deduce whether the law of conservation of momentum is obeyed.

The collisions between electrons and the protons in these experiments are sometimes inelastic.

State what is meant by an inelastic collision.

A potential difference is applied across two parallel plates. A particle carrying a charge of +0.1 C is placed between the plates and experiences a force F.

The distance between the plates is halved. The potential difference remains constant.

Which of the following is now equal to the electric field strength between the plates?

The diagram shows two parallel metal plates with a potential difference (p.d.) of 100 V across them. Three equipotential lines are shown.

Draw lines to represent the electric field in the shaded area.

A parallel plate capacitor consists of a thin layer of insulator of thickness d between two plates of conducting material of area A.

The capacitor has a capacitance 0.1 μF and is charged to a p.d. of 100 V by connecting it to an electrical supply.

The capacitor is then disconnected from the supply and the p.d. between the two plates slowly decreases. This is because the insulator is not perfect and a small charge can flow through it.

The graph shows how the p.d. varies with time.

The insulator is a type of plastic and should have a resistivity greater than 10¹⁴Ω m.

Deduce whether the plastic used in this capacitor has a resistivity greater than this value.

A = 5.6 10⁻³m²

d = 0.6 10⁻⁶m

At the end of the 19th century, J.J. Thompson used electric and magnetic fields to deflect beams of charged particles. A photograph of his apparatus is shown.

Electrons were accelerated through a potential difference to produce a beam of high-energy electrons. The beam was then deflected in perpendicular directions by the magnetic and electric fields. The final position of the beam on the screen was determined by the charge and mass of the electrons.

Explain how electrons from the source become a beam of high-energy electrons.

An electron is travelling left to right and enters a region of uniform magnetic field as shown below. The direction of the magnetic field is perpendicular to the direction of travel of the electron.

The magnetic field deflects the electron in the direction up the page.

Explain the direction of the magnetic field that would produce this deflection.

Explain why the electron would travel in a circular path if no other forces acted on it.

In a modern version of Thompson’s experiment, a uniform electric field of electric field strength E is applied so that the electric and magnetic forces on the electrons are equal and in opposite directions.

Show that for electrons to be undeflected their velocity must be given by

where B is the magnetic flux density of the magnetic field.

The beam is produced by accelerating electrons through a potential difference of 250 V. The electric field strength is 1.4 × 10⁴V m⁻¹. The magnetic flux density is

Calculate the value of the specific charge e/m for the electron using this data.

In his original experiments, Thompson determined the specific charge of a range of particles. His results indicated that the specific charge of an electron is about 2000 times bigger than that for a hydrogen ion.

Deduce what conclusion can be made from this information.

At the end of the 19th century, J.J. Thompson used electric and magnetic fields to deflect beams of charged particles. A photograph of his apparatus is shown.

Electrons were accelerated through a potential difference to produce a beam of high-energy electrons. The beam was then deflected in perpendicular directions by the magnetic and electric fields. The final position of the beam on the screen was determined by the charge and mass of the electrons.

Explain how electrons from the source become a beam of high-energy electrons.

An electron is travelling left to right and enters a region of uniform magnetic field as shown below. The direction of the magnetic field is perpendicular to the direction of travel of the electron.

The magnetic field deflects the electron in the direction up the page.

Explain the direction of the magnetic field that would produce this deflection.

Explain why the electron would travel in a circular path if no other forces acted on it.

In a modern version of Thompson’s experiment, a uniform electric field of electric field strength E is applied so that the electric and magnetic forces on the electrons are equal and in opposite directions.

Show that for electrons to be undeflected their velocity must be given by

where B is the magnetic flux density of the magnetic field.

The beam is produced by accelerating electrons through a potential difference of 250 V. The electric field strength is 1.4 × 10⁴V m⁻¹. The magnetic flux density is

Calculate the value of the specific charge e/m for the electron using this data.

In his original experiments, Thompson determined the specific charge of a range of particles. His results indicated that the specific charge of an electron is about 2000 times bigger than that for a hydrogen ion.

Deduce what conclusion can be made from this information.

State how the bee might use this to detect the electric field of a flower.

State the effect of a decreased electric field strength on the equipotential lines.

A current / and a magnetic field of flux density B are applied to a slice of semiconductor

Calculate the angle of the Earth’s magnetic field to the horizontal.

A potential difference V is applied across two parallel plates. An electron midway between the two plates at point X experiences an electric force F.

The electron moves to point Y which is halfway between point X and the left-hand plate.

Which of the following is the electric force experienced by the electron at Y?

Electric and magnetic fields can be used in particle accelerators.

Which row in the table correctly describes the use of electric and magnetic fields in the particle accelerator indicated?

Sketch the electric field around a positive point charge.

A magician did a trick which he claimed was the most dangerous ever. He positioned himself midway between two charged spheres which were separated by a distance of about two metres. Each sphere was charged to a potential that would cause ionisation at a distance of one metre. He wore a protective suit of chain mail and a helmet consisting of a metal cage. The protective suit and helmet were earthed to a potential of 0 V.

A scientist said “there is no danger in this and I would happily do it tomorrow”.

Explain whether this statement is justified.

Proton beam therapy is being introduced in the UK as a new cancer treatment.

A beam of protons is accelerated by a cyclotron to an energy of 23 MeV and is then focused onto a tumour.

*(a) Explain how the cyclotron produces the high‑energy proton beam.

Conventional treatment may use X‑rays to deliver energy to a tumour.

The graph shows the variation of energy delivered with penetration below the skin for a beam of protons and a beam of X‑rays.

Deduce why the beam of protons could be a more effective treatment for tumours than a beam of X‑rays.

Developing new cancer treatments is expensive.

Give two possible reasons why money should be provided for the development of this new cancer treatment.

Motors usually have a rotating component which can do work W.

In the diagram below, electric field lines have been drawn around one pair of these spheres.

Add to the diagram to show • the directions of the field lines • the lines of equipotential.

The distance between the centres of each charged sphere in this pair is 5.0 cm.

Show that the force between this pair of charged spheres is about 0.04 N.

charge on each sphere = 0.10 μC

The table shows the typical power and the corresponding angular velocity required for three different appliances.

Deduce which of these appliances, in principle, could use the electrostatic motor in (b).

You should use the word equation in (a) and assume that the length of the rod in the electrostatic motor is 8.0 cm.

Assume that the electrostatic motor would deliver a constant force throughout one complete rotation.

Mass spectrometry is a technique used to separate ions based on their charge to mass ratio.

The atoms in a sample are ionised and then accelerated and formed into a fine beam. This beam is passed into a region of uniform magnetic field and the ions are deflected by different amounts according to their mass.

Analysis of mass spectrometer data shows that chlorine exists in nature as two isotopes, chlorine-35 and chlorine-37.

State what is meant by isotopes.

In a mass spectrometer, chlorine-35 ions are accelerated through a potential difference of 8.50 kV to produce an ion beam.

Show that the speed of singly ionised chlorine-35 atoms is about 2.2 × 10⁵ m s⁻¹.

mass of an ion of chlorine-35 = 34.97 u

In most mass spectrometers the ions are passed through a velocity selector, after being accelerated, to produce a beam of ions of a particular velocity. The velocity selector consists of a pair of parallel plates, across which a potential difference (p.d.) is applied to create an electric field.

In one mass spectrometer the plates are 2.5 cm apart and a p.d. of 135 V is applied.

A magnetic field is also applied to produce a force on the ions in the opposite direction to the force from the electric field. For one particular speed the ions travel in a straight line and emerge from the selector.

Add to the diagram to indicate the directions of the electric field and the magnetic field.

The magnetic flux density applied to the velocity selector is 24.5 mT.

Deduce whether this magnetic flux density is suitable to produce a beam of chlorine-35 ions of speed 2.2 × 10⁵ m s⁻¹.

After passing through the velocity selector the ion beam enters a region of uniform magnetic flux density 0.35 T with the ions travelling at right angles to the field direction.

Explain why the ions travel in a circular path.

Calculate the radius of the circular path.

The diagram shows the path of the chlorine-35 ions in the field. Chlorine-37 ions enter the magnetic field with the same velocity.

1. Add another line to the diagram to show the path of these chlorine-37 ions.

2. Explain any differences in the paths.