Exam IV, Magnetism Prof. Maurik Holtrop Department of Physics PHYS 408 University of New Hampshire March 27 th, 2003 Name: Student # NOTE: There are 4 questions. You have until 9 pm to finish. You must staple your Formula-sheet to the back of this exam when handing it in. You are allowed to use your calculator. Work out all problems using variables, then put in numbers. Partial credit can only be given to clearly worked out problems. Useful information: 19 12 2-1 -2 7-1 e = 1.60 10 C ε 0 = 8.85 10 C N m µ 0 = 4π 10 TmA Speed of light: c = 3x10 8 19 6 m/s 1 ev = 1.60 10 J 1 MeV = 10 ev Mass of an electron: M e = 0.5 MeV/c 2 Mass of a proton (approx.): M p =1000MeV/c 2 Problem Description Available Points Score I Short answer Questions 40 II Dipole in field 20 III Particles 20 IV Coax Cable 20 Total Page 1 of 8
I) Short Answer Questions. a) Draw the magnetic field lines (and direction of the field) due to the current in the wire on the two pictures below. I I b) Draw the magnetic field lines for the solenoid in the picture below. (This is a cross section of the solenoid, the windings loop out of and into the page.) I c) The circular region in the picture has a uniform magnetic field inside the circle and no field outside the circle. The magnetic field changes as a function of time as = 0 t. Draw the induced electric field lines (inside and outside the circle), indicating the direction of the field. =0 = t 0 Page 2 of 8
d) The picture below shows two wires 1 and 2 with current i 1 and i 2 respectively. Current i 1 =3Amp and current i 2 =9Amp. The distance between the wires is 3 mm. Draw the vectors for the force F 1 on wire 1 and F 2 on wire 2. What is the ratio of the forces F 1 /F 2? i 1 i 2 d=3mm e) A certain inductor, not a solenoid, with 100 windings is measured to have a magnetic flux 2 of Φ = 3.2 µ Tm when the current through it is 8mA. What is the inductance of this inductor? (indicate the units!) A C f) The three circuit loops in the picture each consist of concentric circular arcs of radii r, 2r or 3r, and straight radial segments. Each circuit carries the same current. Rank the circuits according to the magnetic field (using > and/or =) that is produced at the center of curvature (the dot), greatest first. g) The picture on the right represents the cross section of a solenoid of radius R s =10cm, which has a changing magnetic field, = 0 t, and four different sets of windings. Windings A are wound around the solenoid on the outside with radius R A =15cm. Windings and C are entirely inside the solenoid, with windings tightly against the solenoid edge (radius R =10cm), and C with a much smaller radius, R C =3cm. Windings D are entirely outside the solenoid, with R D =3cm. All the winding have 10 turns and a resistance of 1Ω. Rank the windings (using > and/or =) according to the magnitude of the induced current, greatest first. A A C D =0 = t 0 Page 3 of 8
i i i A C II) A magnetic dipole consisting of a small circular current loop with radius R=3mm, and current i=10ma, is placed in a uniform magnetic field of strength 0.1T. We do this 3 times, in 3 different orientations, A,, and C. In A the dipole has an angle of 45 degrees with respect to the magnetic field, has an angle of 90 degrees and C an angle of 180 degrees. a) What is the dipole moment µ for this dipole? b) What is the net force (magnitude and direction) on the dipole for each of the 3 orientations? A C c) What is the net torque (magnitude and direction) on the dipole for each of the 3 orientations? A C d) What is the potential energy, U, for each of the 3 orientations? A C Page 4 of 8
III) Inside the experimental apparatus pictured on the right is a constant uniform magnetic field of strength. The box with the magnetic field also contains two metal plates which allow a constant electric field to be created when a potential V is applied to the plate on the left. The distance between these plates is d. A particle can be shot into this box through a small hole in the bottom. d a) (The electric potential is turned off.) Derive (don t copy it from your sheet) the equation for the radius a particle with charge q, mass m and velocity v will have when it is shot into the box. Which direction will a positively charged particle go? V v b) When the potential is turned on, the experimenter can set the voltage such that the particle will go straight through the apparatus and escape through the hole at the other end. Derive (don t copy it from your sheet) the equation for the potential V that is needed to cause a positively charged particle to go straight through. (Check the sign for V). Page 5 of 8
c) The experimenter now tries to determine the mass of an unknown particle. The velocity of the particle is not known either. The magnetic field has a strength of =0.2T and the separation between the plates d is 10cm. First with the potential turned off, the experimenter observes that the radius of curvature of the track in the box is R=6.26 cm. Then slowly turning up the potential, she observes that the particle goes straight through when V=24kV. If the particle has a charge of +1e, what is the mass? Page 6 of 8
C A R 1 R 2 R 3 IV) The diagram shows the cross section of a coax cable, constructed with two cylindrical conductors of radii R 1, R 2, and R 3 as shown above. Assume the inner conductor (r<r 1 ) carries a total uniform current I into the page, and the outer conductor (R 2 <r<r 3 ) carries a total uniform current I out of the page. Assume the region between the conductors (R 1 <r<r 2 ) is vacuum. a) Use ampere s law to find the direction and magnitude of the magnetic field for region A (r<r 1 ). b) Use ampere s law to find the direction and magnitude of the magnetic field for region (R 1 <r<r 2 ). Page 7 of 8
c) Use ampere s law to find the direction and magnitude of the magnetic field for region C (R 2 <r<r 3 ) d) ) Use ampere s law to find the direction and magnitude of the magnetic field for the region outside the coax cable. (r>r 3 ) Page 8 of 8