24 Electric Potential
Work Done by an Applied Force
A particle of charge B q moves B from point i to point f
B in an electric field B by applying a force to it.
During the move B the applied force does work B Wapp
on q
The electric field B does work B W B on q.
By the work - kinetic energy theorem
When the particle B stationary before and after the
move.
Kf and Ki B both zero
In words Ð
The work Wapp done by our applied force during the move
is equal to the negative of the work B W done by the
electric fieldB provided there is no change in kinetic
energy.
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24 Electric Potential
Substitute Wapp B into B Eq. 24-1
Substitute Wapp B into B Eq. 24-7
Wapp B positive Û negative Û zero B depending on
the signs and magnitudes of q Û ∆v.
24-4 I Equipotential Surfaces
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24 Electric Potential
Figure 24-2 B shows a family of B equipotential
surfaces B associated with the electric field B due to
some distribution of charges.
The work done B by the electric field B on a charged
particle as the particle moves from one end to the other
of paths I and II B zero
The work done B as the charged particle B moves from
one end to the other of paths III and IV B not zero B but
has the same value for both these B paths III and IV B
connect the same pair ofB equipotential surfaces.
The equipotential surfaces B produced by a point
charge
or
a
spherically
B
symmetrical
charge
distribution B family of concentric spheres.
Equipotential surfaces B always perpendicular to
electric field lines B E B always tangent to these lines.
FIG. 24-3 Electric field lines
(purple) and cross sections
of equipotential surfaces
(gold) for (a) a uniform
electric field,
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24 Electric Potential
(b) the field B due to a point charge,
(c) the field B due to an electric dipole.
24-5 Calculating the Potential from the Field
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24 Electric Potential
FIG.24-4 A test charge qo moves from point i to point f
along the path in a nonuniform electric field.
During a displacement dS', an electrostatic force qoE
acts on the test charge.
This force points in the direction of the field line at the
location of the test charge.
The differential work B dW done on B particle by a
force F B during B displacement B ds
The differential works B done on the charge B as it
moves through all the displacements B ds along the
path:
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24 Electric Potential
Dropping the subscript B f on Vf.
The potential B V B at any point f B in the electric
field relative to the zero potential at point i.
Let point B i B at infinity B the potential V at any
point f relative to the zero potential at infinity.
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24 Electric Potential
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