24 Electric · PDF file24 Electric Potential 111 Figure 24-2 B shows a family of B...
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24 Electric Potential 109 Work Done by an Applied Force A particle of charge q moves from point i to point f in an electric field by applying a force to it. During the move the applied force does work W app on q The electric field does work W on q . By the work - kinetic energy theorem When the particle stationary before and after the move. K f and K i both zero In words The work W app done by our applied force during the move is equal to the negative of the work W done by the electric field provided there is no change in kinetic energy .
Transcript of 24 Electric · PDF file24 Electric Potential 111 Figure 24-2 B shows a family of B...
24 Electric Potential
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Work Done by an Applied Force
A particle of charge q moves from point i to point f in an electric field by applying a force to it.
During the move the applied force does work Wapp on q The electric field does work W on q.
By the work - kinetic energy theorem
When the particle stationary before and after the move. Kf and Ki both zero
In words
The work Wapp done by our applied force during the move is equal to the negative of the work W done by the electric field provided there is no change in kinetic
energy.
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Substitute Wapp into Eq. 24-1
Substitute Wapp into Eq. 24-7
Wapp positive negative zero depending on
the signs and magnitudes of q ∆v.
24-4 I Equipotential Surfaces
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Figure 24-2 shows a family of equipotential
surfaces associated with the electric field due to some distribution of charges. The work done by the electric field on a charged particle as the particle moves from one end to the other of paths I and II zero The work done as the charged particle moves from one end to the other of paths III and IV not zero but has the same value for both these paths III and IV connect the same pair of equipotential surfaces. The equipotential surfaces produced by a point
charge or a spherically symmetrical charge distribution family of concentric spheres. Equipotential surfaces always perpendicular to electric field lines E 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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(b) the field due to a point charge, (c) the field due to an electric dipole.
24-5 Calculating the Potential from the Field
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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 dW done on particle by a force F during displacement ds
The differential works done on the charge as it moves through all the displacements ds along the path:
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Dropping the subscript f on Vf. The potential V at any point f in the electric field relative to the zero potential at point i. Let point i at infinity the potential V at any point f relative to the zero potential at infinity.
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