Physics 102, Learning Guide 4, Spring Learning Guide 4

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1 Physics 102, Learning Guide 4, Spring Learning Guide 4 z B=0.2 T y a R=1 Ω 1. Magnetic Flux x b A coil of wire with resistance R = 1Ω and sides of length a =0.2m and b =0.5m lies in a plane perpendicular to a magnetic field of strength B =0.2T, as shown in the figure above. (a) What is the magnetic flux through the loop? Key 6. (b) What is the flux if B makes an angle of 30 with respect to the z-axis? What if it is 90? Key 25. HQ 4. (c) Assume the magnetic field is along the z-axis. Suppose it is reduced at a uniform rate until it is entirely turned off after 100µs, as graphed below.

2 Physics 102, Learning Guide 4, Spring B (T) t ( µ sec) What is the induced emf around the loop? What is the resulting current, in magnitude and direction? What happens after t = 100µs? Key 21. HQ Faraday s Law B A R B C θ D A square wire of length l =0.2m, mass m =0.8 kg, and resistance R =0.1Ω slides without friction down parallel conducting rails of negligible resistance, inclined at an angle θ =0.2 radians, as in the figure. The rails are connected to each other at the bottom by a resistanceless rail parallel to the wire, and throughout the region there is a uniform vertical magnetic field of magnitude B =0.1T. (a) What emf is induced across the bar when it slides with uniform velocity v? l

3 Physics 102, Learning Guide 4, Spring Key 20. HQ 1. (b) What current flows through the system and around what path does it flow? Key 7. (c) What is the force (in magnitude and direction) exerted on the bar by the magnetic field? Key 18. (d) Explain quantitatively why the bar s velocity would approach a terminal value v t, and find this value. Key 19. HQ 3. HQ 2. HQ 6. (e) What power is being dissipated in the wire when it moves with speed v? How is the energy conservation law satisfied here? Key 8. HQ 5. (f) How would your previous answers have to be changed if the direction of B were reversed? Key 12. (g) Describe the effect on the wire of a rapid increase of B during a certain time interval (this is the principle behind a suggested mass accelerator ). Key Eddy Currents B is into page A metal pendulum is moving into a magnetic field. (a) What is the orientation of the induced eddy currents? Key 2. (b) What is the direction of the force on the pendulum that results from the eddy currents? Key 3. (c) How would the situation differ for a slotted pendulum? Key 9.

4 Physics 102, Learning Guide 4, Spring Alternating Current Generator A rectangular loop of N turns of length a and width b is rotated with a frequency f in a uniform magnetic field B, as in the figure, with B directed into the page. R =2.5Ω B loop b axis of rotation brushes R=10 Ω a (a) Calculate the induced emf that appears in the loop as a function of time. (This is the principle of a commercial alternating current generator.) Note: This problem requires a tiny bit of calculus,or alternately the relation (cos ωt) =ω sin ωt t. Key 16. HQ 9. HQ 11. HQ 10. (b) Design a loop that will produce an emf of peak value 150 V when rotated at 60 Hz in a magnetic field of 0.5 T. Express the answer by giving the required value of Nab. Key 5. (c) If the loop has a resistance of 2.5Ω and the external load has a resistance R = 10Ω, what is the peak current through the load resistor? (Ignore self induction.) Key 4. (d) What is the peak voltage across R? Key 1.

5 Physics 102, Learning Guide 4, Spring Helping Questions 1. What is the rate of change of area of the loop ABCD? Key 15. HQ Resolve these forces along the plane of the rails. What are the components of the gravitational force and the Lorentz force in this direction? Key Draw a free-body diagram of the forces acting on the wire. Key What is the component of B normal to the loop? Key How much power is dissipated in a resistance R when a current I is passed through it? Key Write the balance of forces when the terminal velocity is achieved. 7. From the graph, what is the rate of change of the magnetic field? Key What is the rate of change of the flux through ABCD? Key Let θ denote the angle between the normal to the plane of the loop and the B field. What is the flux through a single turn of the wire as a function of θ? Key What is θ as a function of time? Key What is the flux through N turns of the loop? Key 27.

6 Physics 102, Learning Guide 4, Spring V peak = I peak R = 120 V. 2. Counterclockwise in the diagram. 3. Opposite to the direction of motion. 4. I peak = V peak /R =12A. 5. Nab =0.80m Φ B = Bab =0.02 Wb. Solutions 7. I = E/R = lvb cos θ/r, only around the loop ABCD, in a counterclockwise direction as viewed from above. 8. P = I 2 R = l2 v 2 B 2 cos θ. R The potential energy that the wire loses as it slides is being changed into additional kinetic energy and resistive heating of the wire. When terminal velocity is reached, check that all the potential energy goes into this joule heating. 9. The eddy currents and the slowing force are greatly reduced. 10. Φ B / t =( lv)(b cos θ). 11. If the field were increased very rapidly, the wire would be driven down the rails and attain a very large velocity. 12. The current reverses, but the force is the same. 13. Φ B = Babcos θ. 14. θ = ωt =2πft. 15. A/ t = lv. 16. E =2πfNabB sin 2πft. 17. P = I 2 R. 18. F = q v B = IlB; horizontal to the left.

7 Physics 102, Learning Guide 4, Spring The Lorentz force which opposes the wire s acceleration down the rails is proportional to the velocity v, sothelargerv is, the larger the retarding force. Therefore a terminal velocity will be reached when 20. E = lvb cos θ. v t = mgr l 2 B 2 sin θ cos 2 θ = m/s. 21. E = (abb) = 200V; I = E t R = 200A going counterclockwise as viewed from above. After 100µs, E = I = B = B cos θ. 23. Along the rails, F grav = mg sin θ and F Lorentz = IlBcos θ. 24. B/ t = T/s. 25. Φ B = AB cos 30 = Wb; 0. N F Lorentz 26. mg 27. Φ B = NBabcos θ.

Electromagnetic Induction Practice Problems Homework PSI AP Physics B

Electromagnetic Induction Practice Problems Homework PSI AP Physics B Name Multiple Choice Questions 1. A square loop of wire is placed in a uniform magnetic field perpendicular to the magnetic lines.