Resource Lesson
Electric Fields: Point Charges
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An
electric field
is the region surrounding a charged particle, Q, where another charged particle with experience either a force of attraction or repulsion. For point charges, the electric field lines are radial, getting ever farther apart as you get farther from the point charge itself. These fields are NOT uniform, but are examples of inverse square fields
E = kQ/r
^{2}
.
Dimensional analysis reveals that the units on E, the electric field strength, should be
E = kQ /r
^{2}
(Nm
^{2}
/C
^{2}
)(C)(1/m
^{2}
)
N/C
Intuitively, the
electric field strength
measures the amount of force, in newtons, experienced by a coulomb of charge when it is placed at a particular position within an electric field.
Electric
field lines
point in the direction in which a positive test charge would respond to the electrostatic force; that is, away from positive charges and towards negative charges. In the following diagram, Q is positive, since the field lines are pointing away from Q. If Q had been negative, then the field lines would have pointed towards Q. Note that field lines are NEVER allowed to cross each other.
Another property of field lines is that they terminate on the surface of a charge - they do not penetrate into the charge. Consequently, there is no electric field within a charged conductor under electrostatic conditions. This fact is illustrated in the diagram of E vs r where it shows that the magnitude of the electric field equals 0 between 0 and r.
The size of two charges can be compared by noting the relative number of field lines surrounding each one. If a second charge with only 8 fields lines was compared to the diagram provided above, then it would indicate that the second charge was only ½ as large, since 8 is half of 16.
Fields between oppositely charged particles are attractive and are elliptical in shape; while fields between similarly charged particles are repulsive and hyperbolic in shape.
oppositely charged particles
left is positive; right is negative
similarly charged particles
both are positive
Physlet Animation:
Electric Field Around Two Point Charges
A convenient way to remember the properties of an electric field are to use analogies to gravitational fields. A
gravitational field
is the region surrounding a massive object in which another object with mass will experience a force of gravitational attraction. One important distinction between electrical fields and gravitational fields is that electrical fields can be both attractive and repulsive; whereas gravitational fields are only attractive. Subsequently, gravitational fields cannot be shielded.
Gravitational Forces
Electrostatic Forces
G = 6.67 x 10
^{-11}
Nm
^{2}
/kg
^{2}
is VERY small
gravity is a weak force
inverse square force
attractive only
k = 9 x 10
^{9}
Nm
^{2}
/C
^{2}
is VERY large
electrostatic forces are strong
inverse square force
attractive and repulsive
Gravitational Field
Electrostatic Field (+ charge)
gravitational field strength, g
g's vector nature points towards the center of the planet
each surface represents a unique value for g
g is measured in N/kg (or m/sec
^{2}
)
electric field strength, E
E's vector nature points away from a positive charge or towards a negative charge
each surface represents a unique value for E
E is measured in N/C
In the chart above, you can see that both fields are
inverse square
relationships. That the electric field strength, E, has the same configuration as the gravitational field strength, g. That in each case, the force experienced by a second object equals the product of either that object's mass times the gravitational field strength or that object's charge times the electrical field strength. The direction of the gravitational field is defined as the direction a second object with mass would be attracted; whereas the direction of an electrical field is defined as the direction a positive test charge would respond.
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