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SOLUTIONS – WM3
Q2213) Yes. The charge inside the cavity will pull the electrons of the metal to the
inside of the shell’s surface, thus charging it with –q. The outside of the shell will
then be left with a charge +q.
Q233) a) The electric potential is the potential energy per unit charge, the electric
field is the force per unit charge. Both are normalized to 1 unit charge, but the
potential energy is a scalar whereas the field is a vector.
b) The electric potential is the electric potential energy divided by a unit charge. Both
are scalars, but while the potential energy depends on our test charge, the potential
does not.
Q238) No. If they could, the potential at the crossing point would be the same for
both lines, and as they are lines that show a constant potential, the two lines would
have to have the same potential everywhere.
Q2316) The relation between V and the electric field is given by
∫
⋅
−
=
b
a
ab
l
d
E
V
r
r
.
This relation can be written as
∂
∂
∂
=
−∇
=
z
z
y
y
x
x
E
E
E
V
E
r
.
If V is known at a point in space,
E
can be calculated. If
E
is know at a point in
space, the general behavior of V can be calculated, but not its absolute value at that
point as only differences in the potential can be calculated with the relation above. If
V is known at a second point, e.g. at infinity, then
E
can be calculated as well.
Q243) The capacitance is reduced by half.
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 Spring '08
 Jordan
 Charge, Electric Potential

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