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Assignment 7
Gravitational and electric fields
Introduction
Aims
This assignment will test your ability to: ? answer multiple-choice questions ? describe practical situations and interpret measurements.
You do not need to have studied the physics that underlies these experiments in order to be able to complete the tasks.
The assessment objectives for the A level that are relevant to this assignment are to: ? apply knowledge and understanding of scientific ideas, processes, techniques and procedures:
? in a practical context ? when handling qualitative data ? when handling quantitative data
? analyse, interpret and evaluate scientific information, ideas and evidence, including in relation to issues, to: ? make judgements and reach conclusions ? develop and refine practical design and procedures.
6
Your tutor will assess the following aspects of your work: ? your application of appropriate physical principles ? your use of appropriate equations ? the accuracy of your calculations ? your use of graphs and drawings where directed ? your use of appropriate units.
Are you ready to do this assignment?
Before you tackle this assignment, ensure that you have studied Section 7 of the course and Chapters 3, 4 and 5 of the textbook. While you are encouraged to do the experiments, this is not essential, since sample data will be given to you. However, if you have your own data, please substitute it.
In addition to the usual writing materials (or computer) you will need a sharp pencil, ruler and protractor, graph paper and a calculator.
The assignment
In calculations, use g = 9.81 m s–2 for the acceleration of free fall unless told otherwise. Data for other questions can be found in the Data booklet, which is linked to Section 6.
1 The mass of the planet Mars is 6.39 × 1023 kg. Its radius is 3.39 × 106 m. The gravitational field strength on the surface of Mars is:
(a) 0.27 N kg–1
(b) 3.71 N m–2
(c) 0.371 N kg–1
(d) 3.71 N kg–1
(1 mark)
2 Two stars of equal mass M are in orbit around one another. They are a distance R apart. See the schematic in Figure 7.1. What is the gravitational field strength at the point A, midway between them?
Figure 7.1 Schematic for Question 2
(a) GRM2
(b) Zero
(c) 2GR2M
(d) 4RG2M
(1 mark)
3 A 5 µF capacitor is charged from a 2 V battery. When fully charged how many electrons are on the negative plate?
(a) 3.13 × 1013
(b) 1.56 × 1013
(c) 6.25 × 1013
(d) 1.25 × 1014
(1 mark)
4 It takes a capacitor 18 ms for the potential difference across it to fall to half the original value, Vo / 2. How long does it take for the stored energy to have fallen to one-16th of its original value?
(a) 18 ms
(b) 144 ms
(c) 36 ms
(d) 72 ms
(1 mark)
5 You will need the data in Table 7.1 for this question.
Table 7.1 Data for Question 5
Option Earth Moon
Mass/kg 6.0 × 1024 7.4 × 1022
The two bodies are 3.8 × 108 m apart (Figure 7.2).
Figure 7.2 Drawing for Question 5
(a) Treating the bodies as point masses, calculate the gravitational field strength at a distance of 3.42 × 108 m from the Earth, on the line that joins them.
(4 marks) (b) Comment on this result; what is the net field strength at that point?
(1 mark)
6 Two charges, both +q, are placed 4 m apart (Figure 7.3).
Figure 7.3 Drawing for Question 6
(a) Calculate the potential due to the two charges at the point
midway between them, in symbol form
(2 marks)
(b) Calculate the potential due to the two charges at a distance of 1 m from one of the charges on the same line
(2 marks)
(c) If the electric potential was measured as 50 V at the midpoint, what will it be 1 m from one of the charges?
(2 marks)
7 A point charge of 5 µC is located at point A between two plates 40 cm apart. The potential of the upper plate is 1000 V and the lower plate is at zero. The geometry of the situation is shown in Figure 7.4.
Figure 7.4 Schematic for Question 7
(a) Calculate the force on the charge when it is at A.
(2 marks) (b) Calculate the force on the charge when it is moved to position B.
(2 marks) (c) Calculate the energy that is expended in moving the charge from point A to point B.
(2 marks) (d) Calculate the energy that is expended in moving the charge from point A to point C.
(2 marks) (e) What is the net energy change if the charge is taken around
the loop from A to B, then to C and back to A.
(2 marks)
8 Millikan’s oil drop experiment was replicated in the laboratory (Figure 7.5). The droplet radius was 7 × 10–7 m, and the density of the oil was 900 kg m–3.
Figure 7.5 Schematic for Question 8
The plates were spaced 6 mm apart. When a potential difference of 500 V was applied to the plates, the oil droplet was observed to be stationary.
(a) Draw the two plates, and sketch in, to scale, the equipotential lines where V = 200 V and V = 400 V.
(2 marks) (b) Make a second drawing, and mark in the electric field lines between the plates.
(2 marks)
(c) Calculate the charge on the oil drop.
(4 marks)
(d) Comment on the most likely measurement to be responsible for the discrepancy between the calculated charge and the accepted value of the charge on the electron.
(2 marks) (e) If the potential difference is raised above 500 V what will happen to the oil drop?
(1 mark)
9 The basis for separation of many materials, ranging from ores to recycled plastics, is by electrostatic charge. The materials are ground and charged. They are then allowed to fall through an electric field. Charged particles are deflected in the field and land in different hoppers. A simplified diagram of part of this process is shown in Figure 7.6.
Figure 7.6 Schematic for Question 9
The electric field is supplied by two plates 4 m long, held vertically, and 0.4 m apart. The potential difference between them is 60 kV.
(a) If you assume that the velocity of an ore particle is zero when it enters the area between the plates, how long does it take to fall to the bottom of the plates?
(2 marks)
(b) If the ore particles gain a specific charge 1.6 × 10–6 C kg–1, find the acceleration of the particles in the horizontal direction.
(2 marks)
(c) Hence calculate the horizontal deflection of the charged particles when they reach the bottom of the plates. Give your answer to two significant figures.
(2 marks)
10 A circuit is assembled as shown in Figure 7.7. The capacitance of item C is 4.7 µF.
Figure 7.7 Diagram for Question 10
Measurements of potential difference across C as a function of time are shown in Figure 7.8.
Figure 7.8 Graph for Question 10
Use the graph to estimate the following:
(a) the time it takes for the potential difference across the
resistor and the capacitor to become equal
(2 marks)
(b) the value of the time constant for this circuit
(3 marks) (c) the value of the resistance R.
(3 marks)
11 Figure 7.9 shows a graph of potential difference against charge for a capacitor.
Figure 7.9 Graph for Question 11
(a) Use the graph to find the capacitance of the capacitor.
(2 marks) (b) Calculate the energy stored in the capacitor when V = 6 V.
(2 marks) (c) By making calculations at suitable intervals, sketch a graph of energy stored versus Q.
(4 marks)
The capacitor is placed in series with a resistor, and a square wave is applied. The original square wave and the result are illustrated in Figure 7.10
Figure 7.10 Square wave in RC circuit
(d) Sketch the second wave carefully and, beneath it, to the same scale, sketch a third wave where R has been doubled and C has been halved.
(1 mark)
(e) Sketch a fourth wave beneath these where the product RC has been increased by a factor of 4.
(1 mark)
(Total for assignment 60 marks)