22. Electric Potential. Electric Potential Difference Calculating Potential Difference Potential Difference & the Electric Field Charged Conductors. This parasailer landed on a 138,000-volt power line. Why didn’t he get electrocuted?.
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Electric Potential Difference
Calculating Potential Difference
Potential Difference & the Electric Field
This parasailer landed on a 138,000-volt power line. Why didn’t he get electrocuted?
He touches only 1 line – there’s no potential differences & hence no energy transfer involved.
( path independent )
Electric potential difference electric potential energy difference per unit charge
[ V ] = J/C = Volt = V
if reference potential VA = 0.
For a uniform field:
E = F / q
N/C or V/m
Potential energy difference
J/C or V
Electric potential difference
Potential difference VAB depends only on positions of A & B.
Calculating along any paths (1, 2, or 3) gives VAB = E r.
[ V ] = J/C = Volt = V
E.g., for a 12V battery, 12J of work is done on every 1C charge that moves from its negative to its positive terminals.
Voltage = potential difference when no B(t) is present.
Electronvolt (eV) = energy gained by a particle carrying 1 elementary charge when it moves through a potential difference of 1 volt.
1 elementary charge = 1.61019 C = e
1 eV = 1.61019 J
Between human arm & leq due to 1 mV
heart’s electrical activity
Across biological cell membrane 80 mV
Between terminals of flashlight battery 1.5 V
Car battery 12 V
Electric outlet (depends on country) 100-240 V
Between lon-distance electric 365 kV
transmission line & ground
Between base of thunderstorm cloud & ground 100 MV
In an X-ray tube, a uniform electric field of 300 kN/C extends over a distance of 10 cm, from an electron source to a target; the field points from the target towards the source.
Find the potential difference between source & target and the energy gained by an electron as it accelerates from source to target ( where its abrupt deceleration produces X-rays ).
Express the energy in both electronvolts & joules.
An isolated, infinite charged sheet carries a uniform surface charge density .
Find an expression for the potential difference from the sheet to a point a perpendicular distance x from the sheet.
Staight path, uniform field:
Curved path, nonuniform field:
The figure shows three straight paths AB of the same length, each in a different electric field.
The field at A is the same in each.
Rank the potential differences ΔVAB.
Smallest ΔVAB .
Largest ΔVAB .
Potential of a Point Charge
For A,B on the same radial
For A,B not on the same radial, break the path into 2 parts,
1st along the radial & then along the arc.
Since, V = 0 along the arc, the above equation holds.
Only potential differences have physical significance.
R = point of zero potential
VA = potential at A.
Power systems / Circuits
Earth ( Ground )
Automobile electric systems
A long, straight power-line wire has radius 1.0 cm
& carries line charge density = 2.6 C/m.
Assuming no other charges are present,
what’s the potential difference between the wire & the ground, 22 m below?
Potential of a set of point charges:
Potential of a set of charge sources:
An electric dipole consists of point charges q a distance 2a apart.
Find the potential at an arbitrary point P, and approximate for the casewhere the distance to P is large compared with the charge separation.
V = 0
r >> a
p = 2qa
= dipole moment
The figure show 3 paths from infinity to a point P on a dipole’s perpendicular bisector.
Compare the work done in moving a charge to P on each of the paths.
A total charge Q is distributed uniformly around a thin ring of radius a.
Find the potential on the ring’s axis.
Same r for all dq
A charged disk of radius a carries a charge Q distributed uniformly over its surface.
Find the potential at a point P on the disk axis, a distance x from the disk.
Equipotential = surface on which V = const.
V > 0
V < 0
V = 0
The figure show cross sections through 2 equipotential surfaces.
In both diagrams, the potential difference between adjacent equipotentials is the same.
Which could represent the field of a point charge? Explain.
(a). Potential decreases as r1 , so the spacings between equipotentials should increase with r.
= ( Gradient of V )
E is strong where V changes rapidly ( equipotentials dense ).
Use the result of Example 22.7 to find E on the axis of a charged disk.
x > 0
x < 0
Values of E and V aren’t directly related.
V flat, Ex = 0
V falling, Ex > 0
V rising, Ex < 0
In electrostatic equilibrium,
E = 0 inside a conductor.
E// = 0 on surface of conductor.
W = 0 for moving charges on / inside conductor.
The entire conductor is an equipotential.
Their potentials are
If we connect them with a thin wire,
there’ll be charge transfer until V1 = V2 , i.e.,
In terms of the surface charge densities
Smaller sphere has higher field at surface.
Air ionizes for E > MN/C.
Recombination of e with ion
Corona discharge ( blue glow )
Removes pollutant particles (up to 99%) using gas ions produced by Corona discharge.
Corona discharge across power-line insulator.
Laser printer / Xerox machines:
Ink consists of plastic toner particles that adhere to charged regions on light-sensitive drum, which is initially charged uniformy by corona discharge.