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PH504/10/Test
UNIVERSITY OF KENT
SCHOOL OF PHYSICAL SCIENCES
CLASS TEST PH504-A
Friday 12th November 2010
These questions will be marked each out of 25. Answering the four questions should take 40
minutes). Question S4 is printed overleaf.
S1. In some region of space, the scalar electrostatic potential is the following function of
Cartesian coordinates x, y, and z: V(x,y,z) = x2 y + xy2,
where the potential is measured in volts and the distances in meters. Find the electric field at the
point x = 3 m, y = 3 m, z = 3 m. .
[10 marks]
S2. State how capacitance C, charge Q and potential V are related.
Find the potential energy
of a capacitor with C = 1 pF (pico Farad) and charge Q = 1 mC (milli-Coulomb).
[20 marks]
S3 A polythene sheet with relative permittivity r = 2.3 is placed transverse to an electric field
of 1 x 103 V/m. Find the magnitudes of the electric field E, displacement D and polarisation P
within the polythene. What is the surface charge density? (Note the formula D = r E + P).
S1. The electric field is the gradient of -V
The gradient can be expressed in vector form e.g.
V  (V /x,V /y,V /dz)
Since V(x,y,z) = x2 y + xy2
V  (2xy  y 2, x 2  2xy,0)

Therefore E


 V
E  (27,27,0)

S2.
V/m
C = Q/V where V is the electric potential.
Potential energy is U = QV/2 = Q2 / 2C
= 0.5 x 10-6 / 10-12
= 5 x 10 5 J
S3. E0 = 1 x 103 V/m
The dielectric generates a field which opposes the external field, reducing it by the
factor r:
E = E0 / r = 4.35 x102 V/m,
The displacement is the same inside and outside the polythene:
D = D o = o E0 = 8.85 x 10-9 Cm-2,
P = D - o E =5 x 10-9 Cm-2 =  , the surface charge density.