Electric FieldElectric Field

Force at a DistanceForce at a Distance Electric charges act on each Electric charges act on each

other at a distance.other at a distance.• Empty space between Empty space between

chargescharges

• Net force on a chargeNet force on a charge

Force has to act on another Force has to act on another charge.charge.• Specific charge for a specific Specific charge for a specific

value of forcevalue of force

• Value needed for force Value needed for force magnitudemagnitude

FFFE

2

2

r

kQFF

2

2

r

kQFF

Test ChargeTest Charge Introduce an arbitrary positive Introduce an arbitrary positive

test charge of magnitude test charge of magnitude qq..

The force can be calculated The force can be calculated from the charges using from the charges using Coulomb’s law.Coulomb’s law.

The test charge can be moved The test charge can be moved to other points in space to find to other points in space to find the force.the force.

q

q

Field StrengthField Strength The electric field is the electric The electric field is the electric

force per unit test charge.force per unit test charge.• Measured in N/CMeasured in N/C

The field has a value at every The field has a value at every point in space.point in space.• Independent of force valueIndependent of force value

• Parallel to force directionParallel to force directionq

q

q

FE E

Point ChargePoint Charge The field of a point charge is just like the vector force that would act at a The field of a point charge is just like the vector force that would act at a

point near the charge.point near the charge.• Magnitude comes from Coulomb’s lawMagnitude comes from Coulomb’s law 2r

kQE

SuperpositionSuperposition Two point charges of +10. nC Two point charges of +10. nC

are separated by 8.0 mm. Find are separated by 8.0 mm. Find the electric field at a point 4.0 the electric field at a point 4.0 mm perpendicular to the mm perpendicular to the midpoint of the charges.midpoint of the charges.

The electric fields of point The electric fields of point charges add together.charges add together.• Vector additionVector addition

The The xx-components cancel out.-components cancel out. The The yy-components are equal.-components are equal.

• k = 8.99 x 10k = 8.99 x 1099 Nm Nm22/C/C22

• q = 10 x 10q = 10 x 10-9-9 C C

• x = y = 4.0 x 10x = y = 4.0 x 10-3-3 m m Answer: E = 4.0 x 10Answer: E = 4.0 x 1066 N/C N/C

1E

2E

1q 2q

222

221 45sin2

yxr

r

kqEE yy

Screened ChargeScreened Charge Two oppositely charged point Two oppositely charged point

charges of 10. nC are charges of 10. nC are separated by 2.0 mm. Find the separated by 2.0 mm. Find the electric field at a point 20.0 electric field at a point 20.0 mm from the midpoint along mm from the midpoint along the line of the charges on the the line of the charges on the positive side.positive side.

Only the x components matter.Only the x components matter.

• kk = 8.99 x 10 = 8.99 x 1099 Nm Nm22/C/C22

• qq = 10 x 10 = 10 x 10-9-9 C C• rr = 20.0 x 10 = 20.0 x 10-3-3 m m• dd = 1.0 x 10 = 1.0 x 10-3-3 m m

Answer: Answer: EE = 4.5 x 10 = 4.5 x 1044 N/C N/C

1E

2E

1q 2q

21dr

kqEx

22dr

kqEx

Environmental FieldsEnvironmental Fields Electric fields exist from Electric fields exist from

charges in the environment.charges in the environment.

Distance affects the field Distance affects the field strength from point sources.strength from point sources.

Typical field strengths in N/CTypical field strengths in N/C• Radio waves: 0.1Radio waves: 0.1

• Living room: 3Living room: 3

• 30 cm from a stereo: 9030 cm from a stereo: 90

• Fair weather sky: 150Fair weather sky: 150

• Shower (water on): 800Shower (water on): 800

• Thunderstorm: 10,000Thunderstorm: 10,000

• Cell membrane: 10,000,000Cell membrane: 10,000,000

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