Electric fields and field strength

The Earth’s aurora is an atmospheric effect visible in the polar regions.

Electrons in the upper atmosphere initially move vertically downwards along one of the Earth’s magnetic field lines. They are accelerated by an electric field.

These electrons collide with oxygen atoms causing atomic electrons to be excited to higher energy levels. The atomic electrons then return to lower energy levels, releasing photons of green light, red light and ultraviolet.

The accelerated electrons are accelerated by electric fields parallel to the magnetic field lines.

The length of the acceleration region is 20 000 km and the electric field value is 0.2 mV / m. The electric field can be assumed to be uniform.

Calculate the kinetic energy gained by the electrons as they pass through the electric field, in joules.

State and explain the direction of the electric field required to accelerate the electrons downwards.

A simplified energy level diagram for atomic oxygen is shown below.

Determine the wavelength of the green light emitted.

Fully justify your answer.

The horizontal current closest to the Earth produces a magnetic field which can be detected at ground level.

With reference to Fig. 1.1, state and explain the direction of this magnetic field.

Suggest two ways that the horizontal current may affect the atmosphere.

This question is about lightning.

Sheet lightning occurs when there is an electrical discharge between the upper and lower regions of a thunder cloud. The upper regions are positive and the lower regions are negative.

The thunder cloud can be modelled as an ideal parallel plate capacitor with circular horizontal plates.

The data for the capacitor comes from the cloud.

The diagram shows the plates of the model capacitor superimposed on the cloud.

Draw on the diagram to show the electric field lines between capacitor plates.

Suggest why the actual electric field lines of the cloud would differ from what you have drawn.

Calculate the capacitance C of the model capacitor.

Assume the permittivity of the material of the cloud is the same as the permittivity of free space.

Calculate the magnitude of the charge Q on one of the plates of the model capacitor.

Fork lightning is an electrical discharge that occurs between the bottom of the cloud and the surface of the Earth.

Another cloud has a charge of 155 C and is at a height of 2.0 km.

The surface of the Earth has an electrical potential V of 0 V.

Assume the cloud acts as a point charge.

Calculate the magnitude of the electrical potential V between the cloud and the surface of the Earth.

A fork lightning strike has a duration of 25 ms. The cloud discharges at a constant rate. The cloud is uncharged after the strike.

Calculate the number of electrons reaching the ground in 1.0 ms.

Suggest why the magnetic force acting on the proton has a different magnitude at X than at Y

At X, the motion of the proton is instantaneously equivalent to motion in a circle at a constant speed.

Calculate the radius of this circular motion.

1 Calculate the magnitude of the resultant force on the proton at Y.

2 Explain why the motion of the proton at Y is not instantaneously equivalent to motion in a circle at a constant speed.

Calculate the work function of potassium in eV.

This question is about a photoelectron emitted perpendicular to plate E and with an initial kinetic energy of 4.8 × 10^–20 J.

Show that the magnitude of deceleration of this photoelectron is 8.8 × 10¹² m s^–2. (i)

Show that the initial speed of the photoelectron is about 3 × 10⁵ m s^–1. (ii)

Calculate the time t taken by the photoelectron to travel from plate E to plate C.

Using the axes shown below, sketch a graph of kinetic energy E_k against distance x from plate E.

Explain, in terms of photons, what happens to the ammeter reading when light of frequency greater than 6.3 × 10¹⁴ Hz is now incident on plate E.

Fig. 24 shows two horizontal metal plates in a vacuum.

The diagram is not drawn to scale. Electrons travelling horizontally enter the space between the charged plates and are deflected vertically.

The potential difference between the plates is 4000 V. The distance between the plates is 0.08 m. The initial speed of the electrons is 6.0 × 10⁷ m s^–1. The vertical deflection of the electrons at the far end of the plates is x.

The length of each plate is 0.12 m.

Show that the time t taken by the electron to travel this length is 2.0 × 10^–9 s.

Calculate the vertical deflection x of the electron.

The arrangement shown in Fig. 24 is now used to investigate positrons emitted from a radioactive source. The speed of the positrons is also 6.0 × 10⁷ m s^–1.

The initial path of the positrons is the same as that of the electrons in Fig. 24.

On Fig. 24, sketch the path of the positrons between the plates.

Beta-minus particles (electrons) emitted from a radioactive source have a range of speeds.

Describe and explain how a uniform magnetic field can be applied in the space between the charged plates to select beta-minus particles with a specific speed. No calculations are required.

A ball coated with conducting paint has weight 0.030 N and radius 1.0 cm. The ball is suspended from an insulating thread. The distance between the pivot and the centre of the ball is 120 cm.

The ball is placed between two vertical metal plates. The separation between the plates is 8.0 cm. The plates are connected to a 4.0 kV power supply.

Show that the electric force acting on the charged ball is 4.5 × 10^–4 N.

Draw, on the diagram above, arrows which represent the three forces acting on the ball.

Label each arrow with the name of the force it represents.

By taking moments about the pivot, or otherwise, show that x = 1.8 cm.

The diagram below shows two uniformly charged spheres separated by a large distance z.

The radius of the small sphere is x and the radius of the large sphere is y.

Which is the correct distance to use when determining the electric force between the charged spheres?

A z

B x + z

C y + z

D x + y + z

Your answer

Use Fig. 22.2 to propose and carry out a test to show that Q is inversely proportional to d.

Test proposed:

Working:

Use capacitor equations to show that Q is inversely proportional to d.

* Fig. 22.4 shows an arrangement used by a student to investigate the forces experienced by a small length of charged gold foil placed in a uniform electric field.

The two vertical metal plates are connected to a high-voltage supply.

The foil is given a positive charge by briefly touching it to the positive plate.

The angle made with the vertical by the foil in the electric field is given by the expression

where q is the charge on the foil, E is the electric field strength between the plates and W the weight of the foil.

The angle can be determined by taking photographs with the camera of a mobile phone.

Describe how the student can safely conduct an experiment to investigate the relationship between and E.

Identify any variables that must be controlled.

Additional answer space if required.

An electron is released at a distance r from the surface of a positively charged sphere. It is attracted towards the centre of the sphere and moves until it touches the surface.

Which of the following statements is/are correct?

1 The area under the F against r graph is equal to work done on the electron.

A Only 1

B Only 1 and 2

C Only 1 and 3

D 1, 2 and 3

Your answer

Two isolated parallel capacitor plates have an equal and opposite charge. The separation between the plates is doubled. The charge on each plate remains the same but the potential difference between the plates doubles.

Which statement is correct?

A The capacitance of the capacitor doubles.

B The energy stored by the capacitor is halved.

C The permittivity of free space doubles.

D The electric field strength between the plates remains the same.

Your answer

Fig. 20.1 shows a positively charged metal sphere and a negatively charged metal plate.

On Fig. 20.1, draw a minimum of five electric field lines to show the field pattern between the

sphere and the plate.

Define electric potential at a point in space.

A metal sphere is given a positive charge by connecting its surface briefly to the positive terminal of a power supply. The electric potential at the surface of the sphere is + 5.0 kV. The sphere has radius 1.5 cm.