We find in nature that a positive charge repels another positive charge, a negative charge repels another negative charge, and a positive charge is attracted to a negative charge. The magnitude of this attractive or repulsive force is given by Coulomb's law. The inverse-square nature of this force is similar to that for the law of gravity. Unlike the case for gravity, however, the electric force can be either attractive or repulsive.
Sample problem: Compare the electrostatic force between an electron and
proton to gravitational force between them when the two particles are separated
by 0.5x10-10 m.
Solution: This example shows that the gravitational forces between
charged microscopic objects are much greater than the gravitational forces
between them. That's why gravitational interaction is usually neglected in these
problems.
Sample problem:
Honeybees actively foraging in the field have been found
to be electrically charged, due largely to air resistance as they fly. The
charge carried by a bee is
thought to play a significant role in pollination—the bee can detach grains of
pollen from a distance, like a charged comb attracting bits of paper.
If a bee carries a charge of 93 pC and the force
required to detach pollen from an avocado stigma is 4.0x10-10 N,
estimate the maximum distance at which the electrostatic force between a bee and
a grain of pollen is sufficient to detach the pollen.
Solution: To simplify the calculation, we approximate each charge as a
point charge and assume that the pollen has a charge opposite in sign and equal
in magnitude to that of the bee.
Different charge distributions produce different electric fields. The fields for the most common geometries--point charges, plates, spheres, and cylinders--are shown here.
Sample problem: In fair weather, the atmospheric field of the Earth near
the surface is about 100 N/C; it points vertically downward. What will be the acceleration of a grain of dust of mass 10-18
kg carrying a single electron charge?
Solution: It would appear that the electrostatic forces generated by
charge separation between the ground and the clouds is big enough to overcome
the force of gravity and keep the dust particles suspended in air.
Sample problem: Two identical point charges are positioned at
two corners of a square of side r. What is the direction of the electric field
at an adjacent corner?
Solution: This a vector geometry
problem best approached by figuring out the components of the resultant and
using those to figure out the angle.
Sample problem:
Estimate the width of a lightning column, which has a linear charge density of
about –1x10-3
C/m. Assume the electric field at which ionization begins to occur is 3x106
N/C. Assume the electric field at which ionization begins to occur is 3x106
N/C.
Solution: Here we use the expression for electric field due to an
infinite line as a approximation to the lightning bolt.
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