Static Electricity,Electric Forces,Electric Fields

Static Electricity• Static Electricity involves charges “at

rest”.• Fundamental Rule of Charge

–Opposite charges attract –Like charges repel

• 3 methods of charging : friction, conduction, & induction

• Conductors allow electrons to move freely, Insulators do not!

Methods of Charging• Charging by friction – two neutral objects are rubbed

together and become oppositely charged ( the object that gains electrons becomes negatively charged and the one that loses electrons becomes positively charged)

• Charging by induction – a charged object is brought near but not touching a neutral object ( the neutral object gets a temporary charge separation – gets opposite charge near the charged object)

• Charging by conduction – a charged object touches a neutral object so charges are transferred between objects until they reach charge equilibrium, ie. have equal charge (the neutral object gets the same charge)

Electric Forces

FF

FE = electrostatic force, Newtons (N) k = electric or Coulomb’s constant = 9 x 109 Nm2/C2 q1 = charge of the first object, C q2 = charge of the second object, C d = distance between the two charges (center to center), m

q1 q2

d

+ -Coulomb’s Law:

Given 2 charges of magnitude q1 & q2 separated by a distance d, the magnitude of the force that each of the charges exerts on the other is calculated using Coulomb’s Law. The forces can be attractive or repulsive and must be equal and opposite … Newton’s 3rd Law!

+ +q1 q2

F F1 22E

kq qFd

Electric Charges• Electrons have a negative charge• Protons have a positive charge• Charge is measured in “coulombs”• “qo” or “Q” in an equation is used

for charge• 1 electron has -1.6 x 10-19 C of

charge

Electric Fields• Electric fields are the “energy fields” that surrounds any charged

particle”• Any charge placed in this field will experience a force.• Electric fields are vectors (magnitude & direction).• The direction of an electric field is defined by the direction of the force

on a tiny “+” test charge placed in that field. Thus electric fields are always in a direction that is away from “+”

and toward “-”.• Electric Field strength is the force per unit charge and is measured in

units of N/C (Newtons per Coulomb)

o

FEq

E = Electric Field Strength, N/C

F = Electrostatic Force, N

qo = Charge placed in the electric field, C

Electric Field around a Charge Field around a Field around a Negative charge Positive charge

- +

Note - In the formulas on the previous slide and on the following slides q0 and Q are described as follows:

Q = charge of the object causing the electric field, C

qo = test charge or the charge of the object placed in the field, C

Electric Field Strength at a point near a charge

E= electric field strength, N/Ck = electric or Coulomb’s constant (9 x 109)Q = charge causing the field, Cd = distance from the charge to where the field strength is being measured, m

2

2

o

o o

kq QF kQdEq q d

+.Q E

d

Electric Potential Difference• Electric Potential Difference is the potential energy per

unit charge at a given point due to an electric field.• Units: Volts (1 volt = 1 Joule per Coulomb)• Potential Difference is required to make current flow.

o

PEVq

ΔV = Electric Potential Difference, Volts

ΔPE =change in electric potential energy, J

qo= charge placed in an electric field, C

Note: 1 Volt = 1 Joule / Coulomb

Potential Difference at a Point2o

o o o

kq Q dPE Fd kQdVq q q d

PkQVd

Q .d

VP

ΔVP = Potential Difference at a point, V

k = Coulomb’s constant = 9 x 109 Nm2/C2

Q = Charge causing the electric field, C

d = distance between Q and where VP is

being measured, m

Electric Potential Energybetween 2 charges

1 22

kq qPE W Fd dd

1 2kq qPEd

q1 q2d

Work done on a charge

• W- the work required to move a charge through a potential difference, Joules (J)

• - magnitude of the charge placed in the field, Coulombs (C)

• V - potential difference, Volts (V)

PE WV=o oq q

oW=q ΔVSo:

oq

Electric Potential of a charge moving in a uniform electric field

ΔV=Ed∆V = electric potential difference, V

E = electric field strength, V/m or N/C

d = displacement moved along the field lines, m

Note: It must be a uniform electric field! Also there is no ∆PE and thus no ∆V if displacement is perpendicular to the electric field.

-

-

-

-

-

+

+

+

+

+

E

Capacitor – a device used to store charge. Example

of a common simple capacitor:To get more stored charge:

• increase the size of the plates

• decrease the plate separation

• increase the voltage of the battery

Insulator such as air

2 oppositely charged plates

+ -battery

Note: This is an example of a uniform electric field.

Capacitance – the ability of a conductor to store energy in the form of electrically separated charges

QC=V

C = Capacitance, Farads (F)

Q = charge on one plate, C

∆V = Potential difference, V

Note: 1 Farad = 1 Coulomb / Volt

Also, a Farad is a very large unit so usually use μF or pF. (micro = μ = 10-6, nano = n = 10-9, pico = p = 10-12)

Electrostatics Formulas

PkQVd

ΔV=Ed QC=V

1 2kq qPEd

o

PEVq

1 22E

kq qFd

2

kQEd

Note: The top two and next two equations look alike except for d2 vs d. The ones on the left are vector quantities and have d2

while the ones on the right have d and are not vectors.

o

FEq

oW q V

212CPE C V