Parallel plate capacitors & dielectrics

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.

The student decides to plot T against R to obtain a straight-line graph.

Show that the line has gradient = C ln2.

The data points plotted by the student are shown below.

1 Draw a best-fit straight line through the data points and use the gradient of this line to determine C.

2 Use your answer in (ii)1 to calculate the permittivity of the paper.

=........ F m^–1

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.

A student wishes to determine the permittivity of paper using a capacitor made in the laboratory.

The capacitor consists of two large parallel aluminium plates separated by a very thin sheet of paper.

The capacitor is initially charged to a potential difference V₀ using a battery. The capacitor is then discharged through a fixed resistor of resistance 1.0 M.

The potential difference V across the capacitor after a time t is recorded by a data-logger. The student uses the data to draw the ln V against t graph shown in Fig. 22.

Show that the magnitude of the gradient of the line shown in Fig. 22 is equal to

where C is the capacitance of the capacitor and R is the resistance of the resistor.

* Use Fig. 22 to determine the capacitance C of the capacitor. Describe how the student can then use this value of C to determine a value for . In your description, mention any additional measurements required on the capacitor.

A capacitor of capacitance 7.2 pF consists of two parallel metal plates separated by an insulator of thickness 1.2 mm. The area of overlap between the plates is 4.0 10⁻⁴ m². Calculate the permittivity of the insulator between the capacitor plates.

permittivity =........ F m⁻¹

Fig. 21 shows a circuit.

The capacitance of each capacitor is 1000 F. The resistance of the resistor is 10 k. The cell has e.m.f. 1.5 V and negligible internal resistance.

Calculate the total capacitance C in the circuit.

C =........ F

The switch S is closed at time t = 0. There is zero potential difference across the capacitors at t = 0. Calculate the potential difference V across the resistor at time t = 12 s.