Electrical charge & current

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.

An electroscope is an instrument used to measure electric charge.

The diagram shows one type of electroscope.

The diagram below shows the needle of the electroscope when it is negatively charged. The centre of mass, X, of the needle has been marked on the diagram.

Suggest why the centre of mass of the needle is a short distance below the pivot.

A student charges the electroscope by connecting the metal plate to the negative terminal of a high voltage power supply.

They record the deflection angle of the needle for a range of values of the voltage measured using a voltmeter.

Their results are shown in the graph below.

The student concludes that the voltmeter has a zero error of 300 V.

Explain their reasoning.

The capacitance of the electroscope is 20 pF.

Estimate the number of electrons stored on the electroscope when the deflection angle is 45°.

Show that each X‑ray photon produces about 2000 light photons.

The photocathode has a work function of 2.3 eV.

Explain what is meant by the work function.

Calculate the maximum kinetic energy of the electrons leaving the photocathode.

12 X‑ray photons are detected every minute.

Use your answer to (a) to calculate the current I leaving the photocathode. Assume that all the photons of light produce photoelectrons.

State one other assumption you have made to enable you to calculate the current I in (b)(iii).

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.

A current is present in the circuit below.

The resistor is made from a length of wire.

Which row gives the correct charge carriers in the resistor and in the electrolyte?

Your answer

A gamma camera has several important components including a collimator, scintillator and photomultiplier tubes.

Suggest why the collimator needs to be long and narrow.

State the function of the scintillator.

In a single photomultiplier tube, a photon of light produces a 0.32 A pulse of current for a duration of 1.2 ns.

Calculate the number of electrons responsible for this pulse of current.

State one diagnostic application of a gamma camera.

Question 24 is on the next page

Define the time constant of a circuit containing a capacitor of capacitance C and a resistor of resistance R.

By drawing a suitable tangent to the graph in Fig. 6.3, calculate the maximum current in the resistor.

The circuit diagram of an electrical circuit is shown below.

The positive terminals of the batteries are connected together. One battery has electromotive force (e.m.f.) 4.5 V and internal resistance 0.80 . The other battery has e.m.f. 2.4 V and internal resistance 0.50 . R is a coil of insulated wire of resistance 1.2 at room temperature.

The switch S is closed.

On the diagram, draw an arrow to show the direction of the conventional current.

Calculate the current I shown by the ammeter.

The current measured by the ammeter is smaller than that calculated in (ii). This is because the temperature of R increased due to heating by the current.

Without any changes to the circuit itself, state and explain what practically can be done to make the measured current the same as the calculated current..

The diagram below shows the arrangement of the 3 protons inside the nucleus of lithium-6

The separation between each proton is about 1.0 × 10⁻¹⁵ m.

Calculate the magnitude of the repulsive electric force F experienced by the proton P

Explain how protons stay within the nucleus of lithium-6.

A spherical metal dome shown below is charged to a potential of −12 kV.

The dome is supported by a cylindrical plastic rod. The radius of the dome is 0.19 m.

Show that the magnitude of the total charge Q on the dome is 2.5 × 10⁻⁷ C.

The dome discharges slowly through the plastic rod. It takes 78 hours for the dome to completely discharge.

1 Show that the mean current I in the plastic rod is about 9 × 10⁻¹³ A.

2 The average potential difference across the plastic rod during discharge is 6000 V. The rod has cross-sectional area 1.1 × 10⁻⁴ m² and length 0.38 m.

Calculate the resistivity of the plastic.

=........ m

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.

Which electrical quantity has S.I. units ampere-second (A s)?

A charge

B current

C resistance

D potential difference

Your answer

Which is the best value for the elementary charge e in terms of both accuracy and precision?

Your answer

Fig. 6.1 shows a single photomultiplier tube and its internal components. The tube can detect gamma photons in high-energy physics experiments. A single gamma photon incident on the scintillator crystal generates many photons of blue light. These visible light photons travel to the photocathode where they are converted into photoelectrons. The number of electrons is then multiplied in the photomultiplier tube with the help of electrodes called dynodes. A short pulse of electric current is produced at the output end of the photomultiplier tube.

Fig. 6.2 shows a section through the scintillator crystal in air.

The refractive index of the scintillator crystal for visible light is 1.69. The refractive index of air is 1.00. Calculate the critical angle C for this crystal.

Explain why the visible light inside the scintillator crystal follows the path shown in Fig. 6.2.

A high energy gamma photon passing through the scintillator crystal converts some of its energy into visible light photons of mean wavelength 450 nm.

Show that the energy of a single photon of wavelength 450 nm is less than 3 eV.

The photocathode is coated with potassium which has a work function of 2.3 eV. Each emitted photoelectron is accelerated by a potential difference of 100 V between the photocathode and a metal plate, called the first dynode.

Show that the maximum kinetic energy of an emitted electron at the photocathode is very small compared to its kinetic energy of 100 eV at the first dynode.

2000 photoelectrons are released from the photocathode. Each photoelectron has enough energy to release four electrons from the first dynode at the collision. These four electrons are then accelerated to the next dynode where the process is repeated. There are 9 dynodes in the photomultiplier tube. The total number of electrons collected at the anode for each photoelectron is 4⁹.

The pulse of electrons at the anode lasts for a time of 2.5 × 10⁻⁹ s.

Calculate the average current due to this pulse.

The diagram below shows the motion of positive and negative particles in a conducting solution.

Which statement is correct?

A The current in the solution is zero.

B The conventional current is to the left.

C The positive particles are always protons.

D The negative particles are always electrons.

Your answer