2013 Semifinal Exam Part B 8 Question B2 This problem concerns three situations involving the transfer of energy into a region of space by electromagnetic fields.In the first case,that energy is stored in the kinetic energy of a charged object;in the second and third cases,the energy is stored in an electric or magnetic field. In general,whenever an electric and a magnetic field are at an angle to each other,energy is transferred;for example,this principle is the reason electromagnetic radiation transfers energy. The power transferred per unit area is given by the Poynting vector: 5=LExB 0 In each part of this problem,the last subpart asks you to verify that the rate of energy transfer agrees with the formula for the Poynting vector.Therefore,you should not use the formula for the Poynting vector before the last subpart! a.A long,insulating cylindrical rod has radius R and carries a uniform volume charge density P.A uniform external electric field E exists in the direction of its axis.The rod moves in the direction of its axis at speed v. i.What is the power per unit length P delivered to the rod? ii.What is the magnetic field B at the surface of the rod?Draw the direction on a diagram. iii.Compute the Poynting vector,draw its direction on a diagram,and verify that it agrees with the rate of energy transfer. b.A parallel plate capacitor consists of two discs of radius R separated by a distance d<R. The capacitor carries charge Q,and is being charged by a small,constant current I. i.What is the power P delivered to the capacitor? ii.What is the magnetic field B just inside the edge of the capacitor?Draw the direction on a diagram.(Ignore fringing effects in the electric field for this calculation.) iii.Compute the Poynting vector,draw its direction on a diagram,and verify that it agrees with the rate of energy transfer. c.A long solenoid of radius R has N turns of wire per unit length.The solenoid carries current I,and this current is increased at a small,constant rate i.What is the power per unit length P delivered to the solenoid? ii.What is the electric field E just inside the surface of the solenoid?Draw its direction on a diagram. iii.Compute the Poynting vector,draw its direction on a diagram,and verify that it agrees with the rate of energy transfer. Copyright C2013 American Association of Physics Teachers2013 Semifinal Exam Part B 8 Question B2 This problem concerns three situations involving the transfer of energy into a region of space by electromagnetic fields. In the first case, that energy is stored in the kinetic energy of a charged object; in the second and third cases, the energy is stored in an electric or magnetic field. In general, whenever an electric and a magnetic field are at an angle to each other, energy is transferred; for example, this principle is the reason electromagnetic radiation transfers energy. The power transferred per unit area is given by the Poynting vector : S~ = 1 µ0 E~ × B~ In each part of this problem, the last subpart asks you to verify that the rate of energy transfer agrees with the formula for the Poynting vector. Therefore, you should not use the formula for the Poynting vector before the last subpart! a. A long, insulating cylindrical rod has radius R and carries a uniform volume charge density ρ. A uniform external electric field E exists in the direction of its axis. The rod moves in the direction of its axis at speed v. i. What is the power per unit length P delivered to the rod? ii. What is the magnetic field B at the surface of the rod? Draw the direction on a diagram. iii. Compute the Poynting vector, draw its direction on a diagram, and verify that it agrees with the rate of energy transfer. b. A parallel plate capacitor consists of two discs of radius R separated by a distance d  R. The capacitor carries charge Q, and is being charged by a small, constant current I. i. What is the power P delivered to the capacitor? ii. What is the magnetic field B just inside the edge of the capacitor? Draw the direction on a diagram. (Ignore fringing effects in the electric field for this calculation.) iii. Compute the Poynting vector, draw its direction on a diagram, and verify that it agrees with the rate of energy transfer. c. A long solenoid of radius R has N turns of wire per unit length. The solenoid carries current I, and this current is increased at a small, constant rate dI dt . i. What is the power per unit length P delivered to the solenoid? ii. What is the electric field E just inside the surface of the solenoid? Draw its direction on a diagram. iii. Compute the Poynting vector, draw its direction on a diagram, and verify that it agrees with the rate of energy transfer. Copyright c 2013 American Association of Physics Teachers