Electric Forces and Fields

Electric Charge• Let’s review…• Atoms consist of:

– Protons, neutrons, electrons

• Protons have a charge of:– +e

• Electrons have a charge of– -e

• Neutrons have a charge of 0

What is e?

e=1.6 x 10-19C

Unit is the coulomb (C)

This is the smallest charge yet discovered.

Electric Charge

• Intrinsic property of electrons and protons

• Most objects have balanced charges- in order to carry a charge, there must be an imbalance btwn p+ and e- (ionization)

• Can be positive or negative

• Likes repel• Opposites attract

Electric Charge is…

• Charge is conserved- net charge cannot be created or destroyed

• Charge is quantized- must be an integer multiple of e

• q= the charge of an object (unit is C)

Creating Electric Charge• Usually charge is created

through transfer of electrons

• Gain electrons = gain negative charge

• Lose electrons= gain positive charge

• You can do this in 3 ways:– Friction– Conduction– Induction

Charging by friction

• Different objects have different propensities for gaining or losing electrons

• Triboelectric sequence ranks objects-if you rub any 2 objects together, the one on top will lose elecrons and the one on the bottom will gain

• The farther they are apart, the more they will charge

AsbestosFur (rabbit)GlassMicaWoolQuartzFur (cat)LeadSilkHuman skin, AluminumCottonWoodAmberCopper, BrassRubberSulfurCelluloidIndia rubber

Charging by friction

• Using the triboelectric sequence, predict what will happen when a glass rod is rubbed on a piece of silk

• Will a charge develop?• How big will it be?• Which object will be negative?

Charging by Conduction

• Conduction= TOUCHING

• If you touch a charged object to another object, electrons can actually flow from one to the other

Showing Conduction • We can use an electroscope to show charging by conduction• Take a positively charged rod and touch it to the ball on the

top of the electroscope• Which way would electrons flow?• What would be the residual charge on the electroscope?Electroscope

shows SAME charge after conduction

Charging by Induction

• Charged object is brought near but never touches another object

• Because electric charge does not require contact (electric field), you can induce a charge just by proximity with a charged object

Showing Induction• If you bring your + rod near the electroscope, electrons will be

attracted to it and will gather at the ball- this is temporary- once you move it away, the charge is gone

• However, if the electroscope is grounded (attached to the earth which is a pretty good conductor) you could get electrons flowing from the earth and keep a net charge- opposite to charging rod!

Induction in insulators

• In an insulator, electrons can’t move freely • You can still induce a charge by polarizing

the molecules close to the charged object

In this insulator the top surface becomes - and the bottom surface becomes +

Induction in insulators

• Try this with a charged rod and tiny scraps of paper (an insulator)

• What happens to the paper? Why?

• What processes are happening?

Coulomb’s Law

• Electrostatic force, Fe depends on

• The charge on the objects: q1 and q2

• The distance between them, r

Coulomb’s Law

• For point charges

• F=k q1q2

r2

• On your green sheet, k is written as:

• k= 1/40 but in the section on constants, you can find k- look it up now

• Easiest to deal with magnitudes of q and then note that likes repel, opposites attract

Coulomb’s Law, visually

Example: Coulomb’s Law

• Consider 2 small spheres, one carrying a charge of +1.5nC and the other a charge of -2.0nC, separated by a distance of 1.5cm. Find the electric force between them.

• (reminder: nano=10-9)

Solution: Coulomb’s Law

• FE=kq1q2/r2

• =(9x109Nm2/C2) (1.5x10-9C)(-2.0x10-9C) (0.015m)2

• =-1.2x10-4N

• When F is -, it means attraction…but you knew that already by the opposite charges

• Worksheet: Coulomb’s Law

Superposition and Coulomb

• If there are more than 2 point charges, the FE is the sum of all FE acting on a point

Worksheet: Coulomb Beyond the Fundamentals

and Suspended spheres

The Electric Field

Electric Field

• The presence of a charge created an electric field in the space that surrounds it

• Other charges will be affected by this field

• Directional so it is a vector and can be added/subtracted as a vector

E=Fon q/q

The Electric field equals the electric force on a small test charge, q, divided by that small test charge.

Unit: N/C

Direction: same as force

The electric field leads to the F

Putting it together: FE and E

• FE=kq1q2/r2 • E=Fon q/q

E=Fon q/q

E=kqQ

r2q

E=kQ/r2 Note- not on green sheet. You will need to be able to derive this if you need it!

Electric Field Lines

• Point in for -source• Point out for

+source

• Density of lines shows strength of field

Begin at +, end at -, do not start or stop in midspace, number of lines is proportional to the charge.

Distance and Strength of E

Vector Nature of E

At any point, you can add the EB+EA

Vector Addition of E

Common E interactions

• Note direction of arrows• 2 equal but opposite charges (above right)

are called an electric dipole• NOTICE- fields lines NEVER CROSS

Electric Field Example

• A charge of q=+3.0nC is placed at a location at which the electric field has a strength of 400N/C. Find the force felt by the charge q.

Electric Field Solution

• Fon q=qE

• F=(3x10-9C)(400N/C)=1.2x10-6N

• Worksheet: Electrostatic Forces and Fields: Point Charges

Conductors and Insulators

• Conductors permit the flow of excess charge• Insulators don’t let electrons flow• Semiconductors- kind of in between • Superconductors- no resistance to flow of

electrons (many metals act this way at low T)

Conductors- a closer look

• Any excess charge resides solely on the outer surface of a conductor

• The charge inside is zero!• Any LOST fans? Michael Faraday built a “room

within a room” to demonstrate this- the man in the picture is safe- no charge inside his cage

• We use this to “shield” our sensitive electronics by enclosing in a metal box

Faraday Cage

Conductors- a closer look

• For points outside the conductor, the electric field acts as if it is concentrated at the center of the conductor

• Electric field is always perpendicular to the surface– No matter what the

shape

Special Situations: Parallel Plates

• Above you see 2 parallel plates attached to a battery

• The symbol on the left is the battery- the longer line is the + terminal and the shorter line is the –

• Thus the top plate is + and bottom is –

• The electric field then is the the direction a + charge would move- thus the arrows

Special Situations: Parallel Plates

• This type of field is uniform

• In parallel plates, E=V/d where V is voltage supplied by battery and d is distance between plates

• (units of V/m= N/C) for E

• Thus a test charge would experience the same force regardless of where it is located in the field

• F=qE ANYWHERE between plates

Example: Parallel Plates

• V=28V and d=0.14 m

• Find the F on a 2nCcharge inserted anywhere between the plates

Plates problem solution

• 1st find E:

• E=28V/0.14m

• E=200V/m

• Or 200 N/C

• 2nd find F

• F=qE

• F=(2x10-9C)(200N/C)

• F=4 x 10-7N

• TOWARD which plate?