Phy207 Exam III (Form1) Professor Zuo Spring Semester 15

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1 Phy207 Exam III (Form1) Professor Zuo Spring Semester 15 On my honor, I have neither received nor given aid on this examination Signature: Name: ID number: #1 14 #15/16 Total Enter your name and Form 1 (FM1) in the scantron sheet. Attempt all problems. Multiple choice questions are worth 5pts each and do ONLY one of the two the essay problems (30 pts). There is a formula sheet attached at the end. This is a closed book exam, you must work independently! No collaboration is allowed. Prohibited items: any electronic devices including cell phones and calculators, pens, backpacks, notes, books. Anyone found cheating during the exam will automatically receive an F grade for the course and sent to the honor s court. Put an X next to your discussion section: [ ] Dr. Mezincescu 5O, 9:30 10:20 a.m. [ ] Dr. Zuo 5P, 11:00 11:50 a.m. [ ] Dr. Zuo 5R, 2:00 2:50 p.m.

2 For the next two questions, consider two positive charges q and q moving with v and v respectively, as shown. 1. Find the magnetic field at the midpoint P? A) 0 B) C) D) E) into the page out of the page into the page into the page 2. Find the magnetic force on q due to q? A) down, B) up, C) down, D) up, E) down 3. Find the magnetic field at the center of the semicircle P. A) B) C) D) E) 0

3 For the next two questions, consider three parallel wires each carrying a current I in the direction as shown. 4. Find the magnetic field at the site of middle wire A) B) C) D) E) 0 5. Find the magnetic force acting on the top wire per unit length A) B) C) D) 0 E) None of above For the next 2 questions, consider a coaxial cable consisting of two concentric cylindrical conductors. The inner one is a solid conductor of radius a and the outer one is a conducting shell of inner radius b and outer radius c. They carry equal but opposite currents I, as shown. The current is distributed uniformly cross each conductor. 6. Find the magnetic field at a point. A) B) C) D) E) 0 7. Find the field at a point r (a<r<b) between the two conductors. A) B) C) D) E) 0

4 For the next two questions, consider the circuit shown below. The capacitor is initially charged to Q 0. The switch S is closed at t=0, the capacitor is discharging through the resistor R 0 with the current given by /. 8. Find the direction of the induced current in the small loop A) C.W. B) C.C.W. C) Out of paper D) Into the paper E) None 9. The force between the two loops can be described as A) Attractive B) Repulsive C) No interaction D) Not enough information is given E) None of above For the next three questions, consider a rectangular loop of width L and a slide wire with mass m are shown below. A uniform magnetic field B is directed into the page. The slide is given an initial velocity v o to the right and released. There is no friction between the slide wire and the loop and the loop has negligible resistance compared to the resistance R of the slide wire. 10. Find the induced current in the loop when the loop is moving at velocity v. A) BLv/R, C.W. B) BLv/R, C.C.W C) BLv o /R, C.W. D) BLv o /R, C.C.W E) No current 11. Find the magnetic force acting on the slide wire when it is moving at velocity v. A) B 2 L 2 v/r, to the right B) B 2 L 2 v/r, to the left C) BLv, to the right D) BLv, to the left E) Zero 12. Assuming the slide wire is released at t=0, the velocity at a later time t can be described by A) B) C) D) E)

5 13. The long straight wire carries a constant current I, as shown. A metal bar with length L is moving at a velocity v to the right. What is the magnitude of the motional emf and which end is at higher potential? A), a higher B), b higher C), a higher D), b higher E) None of above 14. A rectangular loop of cross sectional area A is rotating about y axis at constant angular velocity. What is the magnetic flux going through the loop when the induced emf is at maximum? A) BA B) BA C) 0 D) BA/2 E) None of above

6 Choose ONLY one of the two essay questions 15. In the figure shown, the loop is being pulled to the right at constant speed v(loop and the current carrying wire in the same plane). A constant current I flows in the long wire in the direction indicated. A) Calculate the total magnetic flux going through the loop when the left side is a distance r from the long wire. B) Find the magnitude and direction of the induced current in the loop assuming the loop has a resistance R. C) Find the magnitude and direction of the force necessary to keep it moving at the constant velocity. A) B) ln The induced emf is positive, and the induced current, direction is c.w., as shown. The direction can also be derived from Lenz s law, since the flux is decreasing, the induced current should create an induced field in the same direction as the original field (into the page), so it should be c.w. C) When the loop is moving to the right, there is an induced current in the loop. Current carrying segments experience magnetic force in the form of,, pointing toward left. To keep it moving at constant velocity to the right, a counter force to balance the magnetic force is required. The direction of the applied force is to the right.

7 16. A long, straight wire with a circular cross section of radius R carries a total current I o. The current density is not uniform across the cross section, but rather varies as, where is a constant. A) Find the total current I o in terms of α and R. B) Using Ampere s law to calculate the magnetic field for r<r. C) Find the magnetic field outside of the wire (r>r). D) Find the magnetic flux going through the shaded area. A) The total current is given by B) Because of the cylindrical symmetry, the Ampere s law can be applied to calculate the magnetic field everywhere. For a point inside the wire r<r C) Outside the wire, the current in the Ampere s law is the total current I o, so 3 D) The flux going through the shaded rectangle has to be integrated because of the r dependence of the magnetic field.

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