Electric Fields and Capacitors Solutions
Physical Concepts
1. What is an electric field, and what does it tell you?
A vector function of position indicating the strength and direction of the
electric force on a charged object.
2. What are “lines of force,” and what force is it?
Indicate the direction of a force on a positive test “charge”; their density
indicates the strength of this force. They are useful for describing the
effect of any non-contact force.
3. Electric field lines are drawn
(a) from positive charges to negative charges
4. How is intensity indicated in a field map?
By the density of the field lines.
5. What are equipotentials, and how are they experimentally determined?
What is their relationship to electric field lines?
Locations in space at which a test “charge” feels the same field strength
and direction. They are places of equal potential energy, or, in terms of
electrostatics, of equal voltage, and so can be identified with a voltmeter.
Curves connecting equipotential points are always perpendicular to the
field lines.
6. Directions of fields are indicated on field lines. Why are no directions
indicated on equipotential lines?
Potential energy is a scalar, not a vector, quantity.
7. How much work is done in moving a charge of 10 microcoulombs 1 meter
along an equipotential of 10 volts?
0, since moving along an equipotential requires no work.
8. Explain how a gravitational field might be mapped. Sketch the gravitational field for two point masses a short distance apart.
An electric field may be mapped by determining its equipotentials with,
say, a voltmeter. A gravitational field of a very large object may be
mapped by determining its equipotentials by releasing a small object at
various heights above the surface and comparing velocities at impact. For
a small (volume) mass, the deflection of a pendulum or spring loaded
probe might measure the field strength directly.
Such a field, of two point masses, looks exactly like that of two negative
charges:
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