Electric Fields

Montwood High School

AP Physics C

R. Casao

Electric Fields

• The space around every electric charge is filled with an electric field which extends through space.

• Every charge can exert forces on other charges around it without actually being in contact with the other charges and this force This is an example of a field force and can be determined using Coulomb’s law.

• The force that one charge exerts on another can be describes as the interaction between one charge and the electric field set up by the other charge.

Electric Fields

• An electric field is a vector quantity (has both magnitude and direction).– Its strength

(magnitude) is measured by its effect on charges located in the field.

– Small positive charges are used as “test” charges to determine the strength and direction of the electric field produced by a charge at a point in space.

Electric Fields• The direction of the electric field at any point

is the direction of the electrical force on a small positive test charge placed at that point.– If the charge that sets up the field is positive, the

electric field vector points away from the charge.– If the charge that sets up the field is negative, the

electric field vector points toward that charge.

• The electric field vector E at a point in space is defined as the electric force F acting on a positive test charge placed at that point divided by the magnitude of the test charge qo:

oq

FE

Electric Fields• Note that E if the field produced by

another charge that acts on the test charge qo; not the electric field produced by qo.

• The vector E has the units of N/C.

• An electric field exists at a point if a test charge placed at rest at that point experiences an electric force.

• The electric field is said to exist at some point regardless of whether or not a test charge is located at that point.

Electric Fields• When E = F/qo is applied, assume that

the test charge qo is small enough so that it does not disturb the charge distribution responsible for producing the electric field at that point.

• The strength of the electric field is the same for all points that are an equal distance from the charge.

Electric Fields• Consider a point charge Q located a distance r

from a point charge qo.– Coulomb’s law:

– Electric field:

– The electric field at the position of qo is produced by the charge Q.

• To determine the electric field due to a group of point charges, determine the electric field vectors at the point individually and then add them as vectors. The total electric field due to a group pf charges equals the vector sum of the electric fields of all the charges.

2o

rQqk

F

2o

2o

o rQk

qrqQk

qF

E

Charge Density• If a charge Q is uniformly distributed throughout a

volume V, the charge per unit volume is defined as:

• Unit for is C/m3.• If a charge Q is uniformly distributed on a surface of

area A, the surface charge density is defined as:

• Unit for is C/m2.• If a charge Q is uniformly distributed along a line of

length l, the linear charge density is defined as:

• Unit for is C/m.

V

Qρ

A

Qσ

l

Qλ

Charge Density• If the charge is not uniformly distributed

over a volume, surface, or line, we have to express the charge densities as:

where dQ is the amount of charge in a small volume, surface, or length.

dl

dQλ

dA

dQσ

dV

dQρ

Electric Field Lines• A convenient means of visualizing

electric field patterns is with with electric field lines, also called lines of force.

• The electric field lines always point in the direction of the force that would act on a positive test charge qo.– A positive charge is surrounded in all directions by

electric field lines that point away from the charge.– A negative charge is surrounded in all directions by

electric field lines that point toward the charge.

• The electric field vector E is tangent to the electric field line at each point.

Electric Field Lines•The strength of the electric field is indicated by the length of the vectors.•The electric field is greater where the vectors are long than it is where the vectors are short.

Electric Field Lines•The electric field is stronger where the electric field lines are closer together; weaker where the lines are farther apart.

Rules for Drawing Electric Field Lines

For any charge distribution:

1. The lines must begin on positive charges and terminate on negative charges, or at infinity in the case of an excess of charge.

2. The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge.

3. No two field lines can cross.

Electric Field Lines•The charge on the right is negative because electric lines of force go into the charge; the charge on the left is positive because electric lines of force go away from it. •8 lines enter the negative charge; 32 lines leave the positive charge, so the positive charge is 4 times greater than the negative charge.

Electric Shielding• When a car is struck by lightning, the people

inside the car are generally safe. The electrons that strike a metal car repel each other and spread out over the outer metallic surface, finally discharging when additional sparks move from the car’s body to the ground.

• The electric field the charges set up outside the car may be very large; the overall electric field inside the car is almost zero.

• This is true of any charged conductor.• The electric field inside a conductor is zero if

the charges on a conductor are not moving.

Electric Shielding• The absence of an electric field inside a

conductor happens because electrons within the conductor “settle down” and stop moving only when the electric field is zero, so the charges arrange themselves to ensure a zero field with the material.

• The material is attempting to attain equilibrium, which occurs when the arrengement of the charges produces a field of zero inside the conductor.

Electric Shielding• To shield an electric field, surround

the object with a conducting surface. The free charges in the conducting surface will arrange themselves on the surface of the conductor in a way that all the electric field contributions inside cancel each other.

• Electronic components are often encased in metal boxes and some electrical cables have a metal covering to shield them from all outside electrical activity.

Electric Shielding• Another way of determining if the electric field

inside the conductor will be zero is to count the number of electric field lines coming into and leaving the surface, if the number electric field lines coming in equals the number of electric field lines leaving the surface, the net electric field will be zero.

MIT Visualizations• URL: http://ocw.mit.edu/OcwWeb/Physics/8-02TSpring-

2005/Visualizations/Visualizations/electrostatics.htm• Creating an Electric Field• Destroying an Electric Field • Attraction of Charges with Opposite Sign • Repulsion of Charges with Same Sign • The Electric Field of a Positive Charge • Electric Field of a Moving Positive Charge • Electric Field of a Moving Negative Charge • Two Point Charges • The Force on a Charge Moving Through an Electric Field

• The Electrostatic Zoo