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169
Chapter 23
Electrical Potential
Conceptual Problems
*1
•
Determine the Concept
A positive charge will move in whatever direction reduces its
potential energy. The positive charge will reduce its potential energy if it moves toward a
region of lower electric potential.
2
••
Picture the Problem
A charged particle placed in an electric field experiences an
accelerating force that does work on the particle. From the workkinetic energy theorem
we know that the work done on the particle by the net force changes its kinetic energy
and that the kinetic energy
K
acquired by such a particle whose charge is
q
that is
accelerated through a potential difference
V
is given by
K = qV
. Let the numeral 1 refer
to the alpha particle and the numeral 2 to the lithium nucleus and equate their kinetic
energies after being accelerated through potential differences
V
1
and
V
2
.
Express the kinetic energy of the
alpha particle when it has been
accelerated through a potential
difference
V
1
:
1
1
1
1
2
eV
V
q
K
=
=
Express the kinetic energy of the
lithium nucleus when it has been
accelerated through a potential
difference
V
2
:
2
2
2
2
3
eV
V
q
K
=
=
Equate the kinetic energies to
obtain:
2
1
3
2
eV
eV
=
or
1
3
2
2
V
V
=
and
( )
correct.
is
b
3
•
Determine the Concept
If
V
is constant, its gradient is zero; consequently
E
r
= 0.
4
•
Determine the Concept
No.
E
can be determined from either
l
l
d
dV
E
−
=
provided
V
is
known and differentiable or from
l
l
∆
∆
−
=
V
E
provided
V
is known at two or more points.
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170
5
•
Determine the Concept
Because the field lines are always perpendicular to equipotential
surfaces, you move always perpendicular to the field.
6
••
Determine the Concept
V
along the axis of the ring does not depend on the charge
distribution. The electric field, however, does depend on the charge distribution, and the
result given in Chapter 21 is valid only for a uniform distribution.
*7
••
Picture the Problem
The electric field
lines, shown as solid lines, and the
equipotential surfaces (intersecting the
plane of the paper), shown as dashed lines,
are sketched in the
adjacent figure. The
point charge +
Q
is the point at the right,
and the metal sphere with charge
−
Q
is at
the left. Near the two charges the
equipotential surfaces are spheres, and the
field lines are normal to the metal sphere at
the sphere’s surface.
8
••
Picture the Problem
The electric field
lines, shown as solid lines, and the
equipotential surfaces (intersecting the
plane of the paper), shown as dashed lines,
are sketched in the
adjacent figure. The
point charge +
Q
is the point at the right,
and the metal sphere with charge
+Q
is at
the left. Near the two charges the
equipotential surfaces are spheres, and the
field lines are normal to the metal sphere at
the sphere’s surface. Very far from both
charges, the equipotential surfaces and
field lines approach those of a point charge
2
Q
located at the midpoint.
Electric Potential
171
9
••
Picture the Problem
The equipotential
surfaces are shown with dashed lines, the
field lines are shown in solid lines. It is
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This homework help was uploaded on 02/26/2008 for the course PHYSICS 11 taught by Professor Licini during the Spring '07 term at Lehigh University .
 Spring '07
 Licini
 Charge, Energy, Potential Energy

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