課程名稱︰Electromagnetism I
課程性質︰必修
課程教師︰陳俊偉
開課系所︰物理系
考試時間︰Jan 14,2006
試題 :
Final Exam (Close Book)
1.(10 points)
a. The Maxwell equations in the differential form are :
div E = ρ/ε
curl E = - d B / dt
div B = 0
curl B = μJ+με(dE/dt)
where E and B are the electric field and magnetic fields,ρis the electric
charge density and J is electric the current density.ε and μ are constants.
Write the Maxwell equation in the integral form (eg:∮B da =0),explain your
notations,explain the meaning of the equations in English or Chinese and
give a specific example for each equation.
b.Show that the Maxwell equations imply the continuity equation
c.Write the Lorentz force law.
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2) Draw the E field lines for the following configurations:
a.(5 points) An uncharged conducting sphere of radius a is coated with a
thick insulating shell (dielectric constant ε )out to radius b. This object
is then placed in an otherwise uniform electric field E0 .
b.(5 points) The region below abd above the plane z = 0 are filled with
uniform linear dielectric material of susceptibility X and X' respectively.
Draw the E field lines for (i)X > X' (ii) X < X'.
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3 (10 points ) Two infinitely long cylindrical shell with radius a and b are
parallel to each other with distance r between their axes. The cylinders
carries surface currents Ia and Ib respectively. What is the magnetic force
between the two cylinders? (hint: start from solving a simpler problem by
taking b→0 and see what can learn from that.)
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4.( 10 points) A superconducting metal has the property that inside the
superconductor , both B and E are zero.
a. show that the boundary condition at the surface of the superconductor
is that E must be normal to the surface and B must be parallel to the surface.
b.A bar of permanent magnet is above an infinite, superconducting sheet.
The magnet is oriented at an angle θ from the normal. Outline in a few
sentences a method for finding the magnetic field everywhere
(hint : start with θ = 0)
c.At what value of θ the torque in the magnet is zero such that the
configuration is equilibrium? Which angles are stable and which are unstable?
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