Download Tutorial Problem Sheet

JS 3010 Electromagnetism I Tutorial Problem Sheet
1.
Liquid oxygen has a mass density of 1190 kg m-3 and a relative permittivity of
1.5. Use the Clausius-Mossotti Equation to calculate the molecular polarisability
of oxygen.
[ans: 1.92 x 10-29 m3]
2.
For water at room temperature the ratio Eloc/E is 6.6 and the permanent dipole
moment, p, is 6.2 x 10-30 C m. Use the low polarisation approximation to estimate
the electric susceptibility.
[ans: 77]
3.
A block of dielectric (r = 3.2) has dimensions 5 cm square and 12 mm thick. A
total charge of 0.1 micro coulomb (inserted by uniform electron bombardment of
one square face) lies within a 2 mm thick layer which is equidistant from both
square faces. Calculate the bound charge density (a) in this layer and (b) at either
square face of the block.
[ans: (a) +1.38 x 10-2 C m-3 (b) -1.38 x 10-5 C m-2]
4.
The electric field in an LIH dielectric (r = 2.6) makes an angle of 30˚ with the
normal to the boundary with a second LIH dielectric (r = 1.8). Calculate the
angle between the electric field and the normal in this dielectric. [ans: 21.8˚]
5.
GP 1.9 Three charges -q +2q -q which form an electric quadrupole are placed on
a line with equal spacing a (equivalent to two electric dipoles with opposite
sense). Obtain an expression for the potential at the general point (r,) for r>>a.
6.
GP 2.5 Two molecules each have a dipole moment p pointing along their line of
centres with the same sense. How does the force between the molecules vary with
their separation r? What is the potential energy due to the dipole-dipole
interaction when r = 3.1 .10-10 m. p water = 6.2 . 10-30 Cm.
[ans: 1.1 .10-10 N, -2.3.10-20 J]
7.
GP 2.6 If the dipoles in the last problem are free to rotate and take up any
orientation but have their centres fixed. Sketch the orientations of the dipoles
which are in stable or unstable equilibrium.
8.
GP 2.8 A slab of dielectric of relative permittivity  is placed in a uniform
external field Eo whose field lines make an angle  with a normal to the surface
of the slab. What is the density of polarisation charge on the surface of the slab?
Neglect end effects. Find the direction of the field inside the slab and verify your
result using the boundary condition relation tan(1)/tan(2) = 1/2.
[ans:  = o(-1)Eocos /]
9.
GP 4.3 A small sphere is uniformly charged throughout its volume and is rotating
with constant angular velocity. Determine its magnetic moment in terms of the
total charge Q, the angular momentum of the sphere L and its mass M.
m
1
 r x j(r) dr
2 all space
10.
GP 4.5 A long sheet of conductor of thickness 1cm and height 20 cm carries a
current of 104 A distributed uniformly within it. Calculate the magnetic field
along a line ab perpendicular to the surface cutting the sheet half way up (See
figure below). Consider distances from the sheet small compared with 20 cm.
a
I
20 cm
b
1cm
11.
GP 10.1 Positive charge leaves one plate of a parallel plate capacitor which is
discharging through a resistor. At a certain time the rate of change is I Amps.
Calculate the displacement current flowing at this instant through a surface S
which encloses one plate of the capacitor. Show that the magnitude of the
displacement current is equal to the conduction current I.
I
C
S
R
12.
GP 11.2 Show that the time average of the energy density in a monochromatic
linearly polarised plane wave moving in an isotropic non-conducting medium is
distributed equally between the electric and magnetic fields. Show that in a
conducting medium the average energy in the magnetic field is greater than in the
electric field.