SIBT

Phys140, Semester 3, 2014 Lecturer: Dr Levente Horvath

Assignment 4:

This assignment is due in Tuesday Week 12. The assignment should be put in theassignment box. This box is located on the 2nd floor of E3A (at the SIBTs front office).The assessment cover sheet must be attached to your assignment. Late assignments willnot be accepted. Copying some or all assignment questions from other students, or letother students copy some or all of your assignment questions is considered unacceptableand will be rewarded with zero assignment mark!

You must show how you worked out the questions step-by-step where appropriate.

Electrostatics, Magnetism, Electronic Circuits, and Induction

1. (6 marks) Four capacitors with C = 14 F are connected as shown. The potential acrossterminals a and b is Vab = 24 V.

(a) Find the equivalent capacitance between terminals a and b.

Room for working:

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(b) Find the potential across each capacitor.

(c) Find the charge on each capacitor.

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2. (5 marks) Show that the amount of work required to assemble four identical charges (frominfinity (essentially from very far)) of magnitude q1 = q2 = q3 = q4 = qc placed at distances dand 2d (as shown) to a good approximation is 3.144q2c/(4pi0d).

3. (8 marks)

(a) Define voltage and electric field, and explain what 36 V and E = 8k N/C mean?

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(b) Define capacitance, and explain how capacitors work. Write down an expression thatcaptures the relationship between charge and potential difference between the plates of acapacitor.

(c) Derive an expression for the capacitance of the parallel plate capacitor. Assume that thecapacitor carries a +Q charge on one plate and a -Q charge on another plate. Hint: UseGausss Law.

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(d) Explain in detail why a dielectric material increases the capacitance of a capacitor whenplaced between the plates?

4. (5 marks) The figure below shows a section of a long, thin-walled metal tube of radius R = 3 cmwith a charge per unit length = 2 108 C/m. What is the magnitude of the electric fieldat radial distance

(a) r = R/2, and

(b) r = 2R.

(c) Graph E versus r for the range r = 0 to 2R.

Hint: Use Gauss Law and explain all steps in your calculation

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5. (6 marks)

(a) Calculate the speed of a proton that is accelerated from rest through a potential differenceof 45 V to 7 V. The mass of the proton is mp = 1.67 1027 kg, and its charge isqp = 1.60 1019 C.

(b) Calculate the speed of an electron that is accelerated through the potential difference ofVi = 25 V to Vf = 48 V. The mass of the electron is me = 9.11 1031 kg, and its chargeis qe = 1.60 1019 C.

6. (8 marks)

Four charges are placed around the boundary of anisosceles triangle as shown. Assume that q1 = 3C,q2 = 2C, q3 = 1C, q4 = 1C, d1 = 3 cm, andd2 = 4 cm.

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(a) Calculate the electric potential at the point P .

Room for working:

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(b) Calculate the electric field vector at the same point P due to the four charges.

Room for working:

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7. (4 marks) State Kirchhoffs current and voltage laws. Describe these laws in terms of conser-vation of charge and conservation of energy in a circuit.

8. (9 marks) Calculate the current and voltage drops across all components of the followingcircuit. Assume that R1 = 4, R2 = 3, R3 = 5, R4 = 2, R5 = 4, R6 = 8, andV = 16 V.

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Room for working:

9. (9 marks) The emfs and resistances in the given circuit have the following values: V1 = 15 V,V2 = 4 V, V3 = 17 V, r1 = 3, r2 = 2, r3 = 1, and R = 5.

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(a) Find the currents I1 and I2 in this circuit.

(b) Hence, find the potential difference across resistors r1, r2, r3, and R.

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(c) What is the potential difference between the terminals of the batteries? That is find Vab,Vac, and Vcd.

10. (4 marks) Two long straight wires are parallel to each other and spaced 0.05 m apart. Oneof them carry a current of 6 A the other 4 A in (a) opposite direction and (b) same direction.Find the magnitude and direction of forces per unit length between these wires in both of thesecases.

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11. (4 marks) State the Lorentz Force Law, define all the terms, and use it to determine the initialdirection of the deflection of charged particles as they enter the magnetic field moving withvelocity v shown below.

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12. (6 marks)

Eight wires cut the page perpendicularly at the points shown. Awire labeled with the integer k (k = 1, 2, . . . , 8) carries the currentki, where i = 4.5 mA. For those wires with odd k, the current isout of page; for those wires with even k, it is into the page. UseAmperes law to evaluate

~B d~s along the closed path in the

direction shown.

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13. (6 marks)

(a) Describe Amperes law in words and also with an equation. Explain each term in yourequation.

(b) Use Amperes law to find the magnetic field ~B at a distance r from a long wire that carriesa direct current Ic.

(c) Assuming that we have a direct current and all the current flows along the surface of the

wire, find the magnetic field ~B inside the wire. You must explain your answer to getmarks for this question.

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(d) Assuming that we have a direct current and all the current flows along the surface of the

wire, find the magnetic field ~B outside the wire. You must explain your answer to getmarks for this question.

14. (14 marks)

(a) Describe Faradays law of induction in words and also with an equation. Explain eachterm in your equation.

(b) A conducting metal rod ab is in contact with metal rails as shown on the figure below.

A uniform magnetic field ~Bin = 6T (k) is applied everywhere perpendicularly into thepage as shown. The distance between contact points a and b is d = 7 cm.

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i. Find the magnitude of the emf induced in the rod as it moves to the right at a velocity3 m/s to the right.

ii. Explain which end of the rod is at the higher potential.

iii. Explain which direction the current is flowing in the rod.

iv. Draw a clear diagram to show the vector quantities involved.

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(c) If the resistance of the circuit around the loop abcd is 20 find the current flowing in thiscircuit, and the magnitude and direction of the force required to keep the rod moving.

(d) Find the energy dissipated through heat as a result of the magnetic force for the timeinterval t = 8 s.

(e) Repeat part (b) with ~v pointing in the opposite direction (i.e. ~v is 3 m/s to the left).

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15. (4 marks) Use Gausss law to find the electric field inside the cylindrical conductor in anexternal electric field. Write down your derivation step-by-step.

16. (a) (2 marks) Describe the Hall effect. Draw a diagram to illustrate your answer.

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(b) (6 marks) A proton enters into into a region of electric and magnetic fields as shown.

Assume that the velocity of the proton (~v), the magnetic field (~Bin), and the electric field

(~E) are perpendicular to each other.

i. Draw a free body diagram that represent the forces on the proton in these fields.

ii. Find the magnitude of the velocity (|~v|) if the velocity of the proton remains un-changed by these fields for |~B| = 10 T and |~E| = 15 N C1.

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17. (4 marks) Find the equivalent resistance between terminals a and b of the circuit shown belowfor R1 = 6, R2 = 2, R3 = 8, R4 = 1, R5 = 4, R6 = 10, and R7 = 11. Give theanswer to two decimal places.

Room for working:

-Total Marks: 110

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