Faculty of Arts and Science
DECEMBER 2015 EXAMINATIONS
PHY 350H1 F
Duration – 3 hours.
美国物理代考 A magnetic dipole m˙is placed at the centre of a planar circular current loop at an angle θ from the vertical, as shown on figure.
Aids allowed: one 8 1 ”×11” sheet of paper, double-sided, hand- or computer- written
A magnetic dipole m˙is placed at the centre of a planar circular current loop at an angle θ from the vertical, as shown on figure. The current loop has radius R and the current is I. What are the torque and force on the dipole?
Hint: Please use qualitative arguments whenever possible and avoid long-winded derivations.
Total marks for I.: 7 points
Consider the interface between two linear homogeneous magnetic materials with permeabilities µ1 and µ2. Show that, if there are no free currents on the boundary, the B˙-field lines bend at the interface, obeying a kind of magnetostatic “Snell law,” namely that tan θ2 = µ2 , where θ1,2 are the tan θ1 µ1 angles between the normal to the interface and the magnetic field lines. 美国物理代考
Total marks for II.: 9 points
Two compass arrows are free to rotate in the same horizontal plane. They are kept at a fixed distance from each other. How will they choose to orient themselves?
Hint: Treat them as perfect dipoles and pretend the Earth’s magnetic field is absent. Present both qualitative and quantitative arguments to justify your answer.
Total marks for III.: 7 points
Consider two equal same-sign point charges q, placed a fixed distance 2a apart. Use momentum conservation to show that upon integrating Maxwell’s stress tensor over a judiciously chosen surface, the Coulomb force law between the charges is recovered. 美国物理代考
Hint: Make sure to carefully justify every step of the argument.
Total marks for IV.: 10 points
An infinitely long cylindrical tube of radius a moves at a constant speed v along its axis. It carries a net charge per unit length λ, uniformly distributed over its surface. Surrounding it, at radius b, is another cylinder, moving with the same velocity but carrying the opposite charge per unit length −λ.
- Find the energy per unit length stored in the fields.
- Find the momentum per unit length stored in the fields.
- Whatis the energy per unit time “transported” by the fields? Is there an energy flux through any closed surface?
- What is the electromagnetic pressure on each cylinder? Is it positive or negative? Does any special value of v play arole?
Total marks for V.: 13 points
Total marks for the exam 7 + 9 + 7 + 10 + 13 = 46
Total number of pages = 2