Chapter 25Electric Potential

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Chapter 25-Electric Potential

• UNT Physics-2220 Electricity and Magnetism
• 1/28/03

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25-1 Electrical Potential Energy

• Electrostatic force is a conservative force
• U? define as electrical potential energy
• ?U Uf - Ui -W
• Since the electrostatic force is a conservative
  force the work done is path independent.

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Example 25-1
e-
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Units for potential, definition

• Potential 1 Volt1 J/C
• Electric Field
• eV electron volt, defined as the amount of work
  required to move a single charge through a
  potential of one volt. Unit of energy.

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25-2 Electric Potential

• Previously we calculated the potential energy of
  a charge, which depends on the charge.
• We can however define the potential energy per
  unit charge. Units of (J/C). V(U/q)
• example.
• Single positive charge
• V (2.40x10-17 J)/(1.60x10-19C)150 J/C
• Double positive charge
• V (4.80x10-17 J)/(3.20x10-19C)150 J/C
• Thus the potential energy/unit charge is
  independent of the charge of the particle and is
  a characteristic of the electric field only.

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Units for potential, definition

• Potential 1 Volt1 J/C
• Electric Field
• eV electron volt, defined as the amount of work
  required to move a single charge through a
  potential of one volt. Unit of energy.

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25-2 Electric Potential

• V is defined as the electric potential, or most
  of the time just called the potential
• V is a scalar, not a vector. It has no direction
  associated with it
• The potential difference between 2 points is
  just,

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25-3 Equipotential Lines and Surfaces

• Adjacent points that are at the same potential
  form equipotential line and surfaces.
• If we move from one point to another on and
  equipotential surface, we have performed no
  work,regardless of the path taken.
• At any point on an equipotential surface, the
  electric field is perpendicular.
• http//www.electrostatics.20m.com/
• http//www.slcc.edu/schools/hum_sci/physics/tutor/
  2220/e_fields/java/

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Calculating the Potential from the Electric field
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Example 25-2
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Potential Due to a Point Charge
For a positively charged particle
Note The potential goes to infinity as we
approach the charge
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25-6 Potential Due to a group of point charges
25-7 Potential Due to a Dipole
Induced- electric fields can induce dipoles in
matterPermanent - molecules such as water have
permanent dipoles associated with them
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25-8 Potential Due to a Continuous Charge
Distribution

• First choose a differential element dq
• Then determine dV at some point P, due to dq
• Finally just integrate over the charge
  distribution.

Where we have treated dq as a point charge and r
is the distance from P-gtdq
We simply integrate over the charge entire
distribution
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Example - Line Charge
Lambda is the charge per unit lenth
Substitute in and perform the integration
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Example - Line Charge (continued)
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Example - Charged Disk
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Calculating the Electric Field from the Potential
The work done in moving charge some distance ds
We equate both sides and just solve for E
Since the left hand side is just the component of
the electric in the s direction we will just call
it Es
In other words, the component of the electric
field in the direction of s is just the partial
derivative of the potential with respect to s
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Electric Field from the Potential(continued)
For a rectangular coordinate system
For a cylindrical coordinate system
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Example E-Field from the Potential(continued)
The electric potential anywhere on the axis.
The x-component of the electric field for any
point on the x-axis
What are the y and z components, of the electric
field on the x-axis?
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Example Arbitrary Potential
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Electrical Potential Energy of a system of point
charges
The electric potential energy of a system of
point charges is equal to the work that must be
done by an external agent to assemble the system,
bringing each charge in from infinity.
Example
The negative sign indicates it would take work to
pull them apart to infinity
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Potential of an Isolated Conductor

• The electric field inside a conductor will be
  zero, thus the potential will be constant.
• Charge on a conductor will distribute itself so
  that all points within the conductor are at the
  same potential.