Mid Term Exam. Electricity and Magnetism PHY204

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1 Attempt all Question Time Allowed: 2h 15 minutes Mid Term Exam Electricity and Magnetism PHY204 Instructor: Dr. Anzar Khaliq You are provided with a formula sheet. No other formulas outside of that sheet will be provided. Part A consists of MCQ s. You must return it after 30 minutes. Overwriting / Cutting will result in a very nice big zero. Part B contains numerical problems. There is a bonus (optional) problem at the end of part B. It carries extra credits. Part A (weightage in %) Part B (weightage in %) An estimated time per section is provided to help you with time management. Bonne Chance! 1

2 Help sheet k e = = 1 = Nm 2 C 2 4πε 0 = Resistivity of copper = Ω.m ρ Cu ρ Al = Resistivity of aluminium = Ω.m Date: 5 October, 2013

3 Total marks of part A: 30 Time: 30 minutes Mid-Term: Electricity and Magnetism PART A Name: Roll no: Attempt all questions. Circle the appropriate answer. For multiple parts, write down the proper option in front of each part separately. No overwriting/ cutting allowed! 1. An object with negative charge is placed in a region of space where the electric field is directed vertically upward. What is the direction of the electric force exerted on this charge? [1 marks] (a) It is up. (b) It is down. (c) There is no force. (d) The force can be in any direction. 2. A circular ring of charge with radius b has total charge q uniformly distributed around it. What is the magnitude of the electric field at the center of the ring? [1 marks] (a) 0. (b) ke q b 2 (c) keq2 b 2 (d) keq2 b (e) none of these answers. 3. A point charge Q is placed at the origin and another charge 3Q is at r = (a, a, a). What is the net electric flux crossing each of the following Gaussian surfaces; (i) a sphere of radius R = a and (ii) a sphere of radius R = 2a? [2 marks] (a) 2Q ε 0 (b) Q ε 0 (c) 3Q ε 0 (d) Qa2 ε 0 r 2 (e) 2Q(2a)2 ε 0 r 2 (f) 3Q(2a)2 ε 0 r 2 Date: 5 October,

4 Total marks of part A: 30 Time: 30 minutes 4. Car batteries are often rated in ampere-hours. Does this information designate the amount of [1 marks] (a) current, (b) power, (c) energy, (d) charge, (e) potential that the battery can supply? 5. You charge a parallel-plate capacitor, remove it from the battery, and prevent the wires connected to the plates from touching each other. When you increase the plate separation, does each of the following quantities (a) increase, (b) decrease, or (c) stay the same? [10 marks] (i) C. (ii) Q. (iii) E between the plates. (iv) The energy stored in the capacitor. (v) V. How will the answers change for the situation in which the battery remains connected to the capacitor while you increase the plate separation? (i). (ii). (iii). (iv). (v). 6. A filament running along the x axis from the origin to x = 80 cm carries electric charge with uniform density. At the point P with coordinates (x = 80 cm, y = 80 cm), this filament creates potential 100V. Now we add another filament along the y axis, running from the origin to y = 80cm, carrying the same amount of charge with the same uniform density. At the same point P, does the pair of filaments create potential [1 marks] (a) Greater than 200V, (b) 200 V, (c) between 141 V and 200 V, (d) 141 V, (e) between 100 V and 141 V, (f) 100 V, Date: 5 October,

5 Total marks of part A: 30 Time: 30 minutes (g) between 0 and 100 V, (h) 0? 7. A cubical Gaussian surface surrounds a long, straight, charged filament that passes perpendicularly through two opposite faces. No other charges are nearby; (i) Over how many of the cube s faces is the electric field zero? [2 marks] (a) 0. (b) 2. (c) 4. (d) 6. (ii) Through how many of the cube s faces is the electric flux zero? Choose from the same possibilities. 8. A large, metallic, spherical shell has no net charge. It is supported on an insulating stand and has a small hole at the top. A small tack with charge Q is lowered on a silk thread through the hole into the interior of the shell. [5 marks] (i) What is the charge on the inner surface of the shell now? (a) Q. (b) Q/2. (c) 0. (d) Q/2. (e) Q. Choose your answers to the following parts from the same possibilities. (ii) What is the charge on the outer surface of the shell? (iii) The tack is now allowed to touch the interior surface of the shell. After this contact, what is the charge on the tack? (iv) What is the charge on the inner surface of the shell now? (v) What is the charge on the outer surface of the shell now? 9. In a certain region of space, a uniform electric field is in the x direction. A particle with negative charge is carried from x = 20 cm to x = 60 cm. [2 marks] (i) Does the potential energy of the charge-field system (a) increase, (b) remain constant, (c) decrease, (d) change unpredictably? Date: 5 October,

6 Total marks of part A: 30 Time: 30 minutes (ii) Does the particle move to a position where the potentials; (a) higher than before, (b) unchanged, (c) lower than before, (d) unpredictable?. 10. A fully charged parallel-plate capacitor remains connected to a battery while you slide a dielectric between the plates. Do the following quantities (a) increase,(b) decrease, or (c) stay the same? [5 marks] (i) C. (ii) Q. (iii) E between the plates. (iv) V. (v) The energy stored in the capacitor. Date: 5 October,

7 Total marks of part B: 20 Time: 1 hour and 45 minutes Mid-Term: Electricity and Magnetism PART B First four questions are compulsory. Question 5 is optional. Extra marks will be awarded for it. 1. A particle with charge Q is located immediately above the center of the flat face of a hemisphere of radius R as shown in Fig 2. What is the electric flux (a) through the curved surface and (b) through the flat face? [ marks] ( 10 mins) FIG A sphere of radius R surrounds a particle with charge Q, located at its center. ( 20 mins) (a) Show that the electric flux through a circular cap of half-angle θ (Fig. 2) is [3 marks] ϕ e = Q 2ε 0 (1 cos θ) What is the flux for (b) θ = 90 0 [1 marks] (c) θ = 180 0? [1 marks] FIG. 2 Date: 5 October,

8 Total marks of part B: 20 Time: 1 hour and 45 minutes 3. A solid sphere of radius R has a uniform charge density ρ and total charge Q. Derive an expression for its total electric potential energy. Suggestion: Imagine the sphere is constructed by adding successive layers of concentric shells of charge dq = (4πr 2 dr)ρ and use du = V dq. [5 marks] ( 15 mins) 4. Residential building codes typically require the use of 12-gauge copper wire (diameter cm) for wiring receptacles. Such circuits carry currents as large as 20 A. If a wire of smaller diameter (with a higher gauge number) carried that much current, the wire could rise to a high temperature and cause a fire. ( 20 mins) (a) Calculate the rate at which internal energy is produced in 1.00 m of 12-gauge copper wire carrying 20.0 A.[2.5 marks] (b) What If? Repeat the calculation for an aluminum wire with same diameter and length. Explain whether a 12-gauge aluminum wire would be as safe as a copper wire.[2.5 marks] (Bonus (optional) problem) 5. A horizontal, parallel-plate capacitor with vacuum between its plates has a capacitance of 25.0 µ F. A nonconducting liquid with dielectric constant 6.50 is poured into the space between the plates, filling up a fraction f of its volume. ( 30 mins) (a) Find the new capacitance as a function of f.[1.5 marks] (b) What should you expect the capacitance to be when f = 0? Does your expression from part (a) agree with your answer?[1 marks] (c) What capacitance should you expect when f = 1? Does the expression from part (a) agree with your answer?[1 marks] (d) Charges of magnitude 300 µ C are placed on the plates of the partially filled capacitor. What can you determine about the induced charge on the free upper surface of the liquid? How does this charge depend on f?[1.5 marks] Date: 5 October,

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