General Physics 2 Electric Field 1

E2 - Electric Field• Electrostatic & gravitational force

• act at a distance, no direct push or pull

• Electric Field • conceived by Michael Faraday• extends out from every charged object• other charges interact with field• direction of field determined by motion induced on

a positive test charge

General Physics 2 Electric Field 2

E2 - Electric Field• Coulomb’s Law

• Action-at-a-distance model• Charges act directly on one each other

• Electric Field• Field model• Field acts on charge

€

charge ↔ charge

€

charge ↔ field ↔ charge

General Physics 2 Electric Field 3

Electric Field

€

rE ≡

r F eq

€

rF e = q

r E

€

rE =

1

4πε0

q

rPC2

ˆ r PC

• Electric field is a vector expressed in terms of the electric force and the charge

• If Q > 0, E points away from Q • If Q > 0, E points away from Q

Insert fig. E2.1

General Physics 2 Electric Field 4

Magnitude of Test Charge, q0

• The test charge is a conceptual tool to help understand the magnitude and direction of the electric field. • The magnitude of the test charge is VERY small. • The test charge does not affect existing charge distribution

Electric Field: A proton is released in a uniform electric field, and it experiences an electric force toward the south. What is the

direction of the electric field?

1. North

2. South

3. East

4. West

Electric Field: An electron is released in a uniform electric field, and it experiences an electric force toward the west. What is the

direction of the electric field?

1. North

2. South

3. East

4. West

Electric Field:What are the magnitude and direction of the electric force on an electron (e=1.6x10-19 C) in a uniform electric field of strength 2000 N/C that points due east?

1. 3.2x10-16, east

2. 3.2x10-16, west

3. 8.0x10-23, east

4. 8.0x10-23, west

General Physics 2 Electric Field 8

Think-Pair-Share• Calculate the electric field 0.1 m from a

10-6 C charge.

General Physics 2 Electric Field 9

Analogy• Electric field is electric force per unit

charge. What is the analogous quantity for gravitational force? Derive a mathematical expression for gravitational field. Have you seen this quantity before?

General Physics 2 Electric Field 10

Electric Field Lines

• Field lines show the magnitude (in a relative way) and the direction of the force felt by a positive test charge

• Insert E2.2

General Physics 2 Electric Field 11

Electric Field Lines (L)• Draw field lines for the following charge

distributions

- +

General Physics 2 Electric Field 12

Electric Field Lines (L)• Draw field lines for the following charge

distributions

- -

General Physics 2 Electric Field 13

Superposition

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rE =

r E 1 +

r E 2 +

r E 3 + ...

• How do you calculate the electric field due to multiple charges?• Calculate the field due to each

charge and add them up!

General Physics 2 Electric Field 14

Think-Pair-Share (L)

• Two charges, Q1 and Q2, are separated by 100 nm. What is the electric field midway between the charges?

Q2 = 10 x 10-6 C

Q1 = -1x10-6 C

General Physics 2 Electric Field 15

Think-Pair-Share (L)

• Two charges, Q1 and Q2, are separated by 100 nm. Where on the line joining Q1 and Q2 is the electric field equal to zero?

Q1 = 1x10-6 CQ2 = 10 x 10-6 C

General Physics 2 Electric Field 16

Electric Field is a Vector• What is the net Electric field at point A?• What is the net force on a charge Q that

is placed at A?

General Physics 2 Electric Field 17

Electric Field of a dipole• A dipole is a pair of particles separated

by a small distance, equal magnitude and opposite signs

• The field of a dipole decreases with distance more rapidly than a single charge

• Insert E2.4

General Physics 2 Electric Field 18

A dipole has an electric field• A dipole is electrically neutral, so why

does it have a field?• The electric field of the near charge is

longer than that of the far charge• Insert E2.5

General Physics 2 Electric Field 19

Field of the dipole

• Insert E2.6 and E2.7, E2.8• E2.9, E2.10

General Physics 2 Electric Field 20

Torque of a dipole• The torque of a dipole in an external electric

field• d is the distance displacement vector from “-” to “+”

Insert E2.9

€

vτ dp =r d × q

v E = q

r d ×

v E =

r p e ×

v E

r p e ≡ q

r d

General Physics 2 Electric Field 21

Water is a dipole• If water is put in an electric field, the

water molecules will experience a torque that attempts to twist them

• Insert E2.8 and E2.10

Lightning

Hail

Ice Crystals

Upward streamers of + ions travels up from ground. Lightning occurs if it meets stepped leader from cloud.

Interactions b/w hail and smaller ice crystals transfer e- to hail. They are heavier and sink to base of cloud.

Path oflightningis about 1 cm in diameter

Thunder:shock wavecreated by rapidheating of air

e- run away from cloud base, leaving net + charge on ground under cloud

Light due to e-’s recombining w/ions

General Physics 2 Electric Field 23

Lethal Strike• Physiological effects of

a direct strike:• stops heart • paralyzes muscles• internal burns

• Heart may restart, but breathing won’t• need mouth-to-mouth

• Other types of strikes: • Side flash or touching struck object• Ground current• Dead-end upward streamer

General Physics 2 Electric Field 24

Lightning Rods

• Provide path for current to pass directly to ground without passing through building

• path of least resistance• Diffuse charge build-up• Photo from lightning

research center in FL• lightning rods may not

provide enough protection to homes built on sandy soil

General Physics 2 Electric Field 25

Lightning Safety• Lightning kills ~100 people per year in US• Stay inside if possible. Avoid:

• showers• much lower resistance when wet

• phones (cell phones are ok)• any electrical appliances

• If outside, • avoid tall objects• seek low-lying area• duck head, crouch• pull feet together, run, hop on one foot (ground current)• stay in car - Faraday cage (Note: Saturns are not safe!)

General Physics 2 Electric Field 26

Lightning: Physical Characteristics

• Voltage• several hundred million volts

• Current• 1020 electrons in a fraction of a second• ~10 kiloamps

• So what is a Volt? what is an amp?• Good question. We’ll get to that soon.

Electric Field: The electric field just

before a lightning strike points:

1. toward the ground

2. toward the cloud

3. along the ground

General Physics 2 Electric Field 29

Group Problems

• E2B.4, E2B.5, E2S.2