Magnetic Fields unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Choosing an Ampèrian loop
Biot-Savart law
Circular motion in a magnetic field
Ampère's law vs Biot-Savart
Field of a finite wire segment
Field of a long straight wire
Right-hand rules summary
Velocity selector
Force on a current-carrying wire
Field of a toroid
Hall effect
Why magnetic force does no work
Short answer 1. Define or explain: Torque on a current loop
3 ptsShort answer 2. Define or explain: Magnetic dipole
3 ptsShort answer 3. Define or explain: Field at the center of a circular loop
3 ptsShort answer 4. Define or explain: Force between parallel wires
3 ptsFree response
10 ptsMATHEMATICAL ROUTINES (Question 1, 10 points). Two very long cylindrical wires are parallel to the y-axis with centers in the xy-plane (Figure 1). Wire S has radius 2a, is centered at x = 0, carries total current I0 in the +y-direction, and has nonuniform current density J = Cr (C a positive constant, r the radial distance from its center). Wire T has radius a, is centered at x = 10a, has uniform current density, and carries total current I0 in the −y-direction. For B: at the instant shown (Figure 3), a small sphere with charge Q at x = 5a moves in the xy-plane with speed v in the +x-direction; the net magnetic force on it from both wires has magnitude F.
A(i). Point P is inside Wire S at x = a. Derive an expression for the magnitude of the magnetic field at P due only to Wire S, in terms of C, a, and physical constants, as appropriate.
A(ii). Describe the graph of the magnitude B of the magnetic field due to both wires as a function of x along the x-axis for 2a ≤ x ≤ 9a.
B. Derive an expression for F in terms of a, Q, I0, v, and physical constants, as appropriate.