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Electric Fields

Electric field
The area around a charged object. This field exerts a force on any charged object in its vicinity. The closer the charged object is brought to the charged object creating the field, the greater the force exerted on it.

Test charge
a positive charge of very small magnitude. The test charge is used to determine the direction of the electric field.

Electric field lines
The electric field can be represented with electric field lines. Their density is a measure of the strength of the electric field at that point. Their direction is one that a positive test charge would take in the field. Field lines are always directed from the positive charge and toward a negative charge.

Electric field strength (or intensity)
symbol is E and SI unit is N/C; the force on a test charge
formula for electric field

Electric field strength of a point charge:

formula for electric field due to a point charge

where E is the electric field, k is Coulomb’s constant, and d is the distance between the charge and the test charge

Electric field is a vector quantity; it has both magnitude and direction. The resultant electric field due to several point charges can be determined using the same method as was used in Coulomb's Law problems. Calculate the strength of the electric field due to each point charge at point P. Determine the direction of the electric field by determing the direction that a test charge placed at point P would take. Use vectors to determine the magnitude and direction of the resultant electric field at point P.

Electric Potential

Two points are said to differ in electric potential if work is done to move a charge from one point to another point in an electric field.

Potential (symbol is V; SI unit is volt)
work done on a charge; or the electric potential is the potential energy per unit charge. Only differences in potential can be measured.
V = W / q

In a uniform electric field (a parallel plate capacitor):
V = E d
where E is the electric field strength and d is the separation between the plates in meters

The electric potential at a distance r from a single point charge can be derived from the expression for electric field due to a point charge. The expression for absolute potential:

V = k q / r2

Electric potential is a scalar term. When finding the electric potential due to a collection of point charges, you need only add the potentials together with no concern for direction. You must, however, include the signs of the charges when calculating absolute potential.

Millikan’s oil drop experiment
accurately measured the charge of an electron
E q = m g
where E is the electric field, q is the charge in Coulombs, and mg is the weight in Newtons

Sharing of Charge

In a conductor, charges move until all parts of a conductor are at the same potential. If a large and a small sphere have the same total charge, the large sphere will have a lower potential. If a large and a small sphere have the same potential, the large sphere will have the greater charge.

Grounding
the potential of the earth is zero. Any object connected to the earth will have its excess charge flow into the earth. It is considered to be grounded.

Electrostatic charges are only found on the outside of conductors.

Capacitors

Capacitor
a device that stores charge in the electric field between its plates. Each plate carries the same amount of charge, one plate being negative and the other being positive. A potential difference exists between the two plates.

Capacitance
symbol is C and SI unit is the Farad, F
q = C V
where q is the charge in Coulombs, C is the capacitance, and V is the potential difference

It requires energy to place charges on the plates of a capacitor. When the capacitor is discharged, this electrical energy is released.

Energy = ˝ C V2

where C is the capacitance and V is the voltage

When a DC voltage source is connected across an uncharged capacitor, the rate at which the capacitor charges up decreases as time passes. At first, the capacitor is easy to charge because there is little charge on the plates. But, as the charge accumulates, more and more work is needed to move additional charges on the plates because the plates already have charge of the same sign on them. As a result, the capacitor charges exponentially, quickly at the beginning and more slowly as the capacitor becomes fully charged. At any time, the charge on the plates is given by:

charge on a capacitor formula

Half-life
The time it takes the capacitor to reach half full is called the half-life and is related to the time capacitive time constant in the following way:

half-life = RC ln 2

where R is resistance in ohms and C is capacitance in Farads

Electric Field, Electric Potential, and Capacitors Sample Problems

Electric Field, Electric Potential, and Capacitors Homework

Capacitor Major Lab Data Analysis and Questions