Question 1
(a) In no more than 200 words, briefly explain both the similarities and differences between Newton's law of universal gravitation and Coulomb's law.
(b) Consider two point-like objects, A and B, the first of which has four times the mass of the other (i.e. MA = 4MB). They are placed a certain distance d apart.
(i) Sketch (in 2-dimensions) the gravitational field lines that are present in the region of space around the two masses. Show the direction of the field on the field lines.
(ii) Explain quantitatively where you should place a test particle such that it experiences a net gravitational force of zero from the two point-like objects. Indicate this position on your diagram.
Question 2
This question is worth 15 marks, and is designed to test your understanding of electric potential and potential energy.
(a) Two point charges with q1 = +3.2 × 10-7 C and q2 = -4.8 × 10-7 C are initially separated by a distance of r = 2.4 × 10-4 m.
(i) How much energy is required to double their separation?
(ii) What is the electric potential at the point midway between the two charges when their separation is 2r?
(b) A uniform electric field of magnitude 1.0 × 102 NC-1 exists between two conducting plates, one of which is positively charged and the other of which is negatively charged. The plates are 10 mm apart.
(i) Calculate the magnitude of the potential difference between the plates.
(ii) If a proton is moved from the positive plate to the negative plate, what is the magnitude of the change in its electrostatic potential energy?
(iii) Sketch the electrostatic equipotentials between the two plates.
(iv) If this device operates as a capacitor, how is it able to store electrostatic potential energy?
Question 3
(a) State in your own words Kirchhoff's laws and Ohm's law for electrical circuits. (Answers quoted from the module material or elsewhere will receive no marks.)
(b) The circuit shown in Figure 1 can be used to measure the resistance of a platinum resistance thermometer (PRT). AB is a uniform resistance wire of length 1.0m and C is a sliding contact on this wire. A standard resistor R is included in the circuit. The position of C is adjusted until the voltmeter V reads zero.
Figure 1
(i) By applying Kirchhoff's laws to loops ADCA and BCDB, deduce an expression for the resistance of the PRT in terms of l1, l and the value of the standard resistor.
(ii) The PRT consists of 9.0 m of wire of diameter 8.0 × 10-2 mm. The voltmeter reads 0 V when l1 = 0.44 m. If the standard resistor, R, has a resistance of 224 Ω, what is the resistivity of platinum? Show that you have checked that the value for the resistivity and its unit are sensible.
(c) Indicate briefly what factors might affect the precision of the measurement when using such a simple circuit to measure the resistance of the PRT.
Question 4
This question is worth 10 marks, and is designed to assess your engagement with interactive Quiz 3, covering Units 7, 8 and 9. It also allows you to reflect on the feedback you received on TMA 02.
(a) To demonstrate your engagement with Quiz 3, paste into your TMA answers a screenshot from your computer showing the marks you obtained on the Quiz. It does not matter what score you obtained, we are only interested in whether or not you tried the Quiz. Remember also that you may attempt the Quiz questions as often as you wish, and each question has multiple variants that will be presented to you in turn, each time you try it.
(b) In a few sentences, describe one thing that you learned from answering the questions in the Quiz that improved your understanding of gravitational or electric forces, fields or potentials. (If you scored full marks on the Quiz the first time you tried it, then it is acceptable to say that you had nothing further to learn, but in that case we would expect such a statement to be supported by the screenshot in part (a).) You should not need to write more than 100 words to answer this part.
(c) (i) Identify one skill you need to develop that was identified in the general feedback you received on TMA 02 and explain what you have done to develop this.
(ii) Identify a different skill you need to develop that was identified in comments on your submitted answers to TMA 02 and explain what you have done to develop this.
If you received a perfect score on TMA 02 and there were no skills which your tutor identified that you need to develop, then it is acceptable to state this. You should not need to write more than 100 words to answer this part.