Charge•Comes in + and –•Is quantized

•elementary charge, e, is charge on 1 electron or 1 proton

•e = 1.602 10-19 Coulombs

•Is conserved•total charge remains constant

Coulomb’s Law•F = kq1q2/r2

•k = 8.99 109 N m2 / C2

•q1, q2 are charges (C)•r2 is distance between the charges (m)

•F is force (N)•Applies directly to spherically symmetric charges

Spherical Electric Fields

F =kqq0

r2

E = F = kq q0 r2

Why use fields?Forces exist only when two or more particles are present.

Fields exist even if no force is present.

The field of one particle only can be calculated.

Field around + charge

Positive charges accelerate in direction of lines of force

Negative charges

accelerate in opposite direction

Field around - charge

Positive charges follow lines of force

Negative charges go in opposite

direction

For any electric field

F = EqF: Force in NE: Field in N/Cq: Charge in C

Principle of Superposition

When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges.

Field around dipole

Caution…

Electric field lines are NOT VECTORS, but may be used to derive the direction of electric field vectors at given points.The resulting vector gives the direction of the electric force on a positive charge placed in the field.

Field Vectors

Electric Potential

U = kqq0

rV = U = kq q0 r

(for spherically symmetric charges)

Electrical Potential

V = -EdV: change in electrical potential (V)

E: Constant electric field strength (N/m or V/m)

d: distance moved (m)

Electrical Potential Energy

U = qVU: change in electrical potential energy (J)

q: charge moved (C)V: potential difference (V)

Electrical Potentialand Potential Energy

Are scalars!

Potential Difference

Positive charges like to DECREASE their potential.(V < 0)

Negative charges like to INCREASE their potential.(V > 0)

Announcements 04/19/23

Lunch Bunch WednesdayGraded quiz tomorrowExam Friday

Potential surfacespositive

negative

highhighest

medium

lowlowest

Equipotential surfaces

highlow

Today...More with electric potential and potential energy.

Definition: Capacitor

Consists of two “plates” in close proximity.

When “charged”, there is a voltage across the plates, and they bear equal and opposite charges.

Stores electrical energy.

Capacitance

C = q / VC: capacitance in Farads (F)q: charge (on positive plate) in Coulombs (C)

V: potential difference between plates in Volts (V)

Energy in a Capacitor

UE = ½ C (V)2

U: electrical potential energy (J)C: capacitance in (F)

V: potential difference between plates (V)

Capacitance of parallel plate capacitor

C = e0A/dC: capacitance (F)

e: dielectric constant of filling

0 : permittivity (8.85 x 10-12 F/m)A: plate area (m2)d: distance between plates(m)

dielectric

Parallel Plate Capacitor

E

+Q

-Q

V1V2

V3

V4

V5

Cylindrical Capacitor

- Q

+ QE

Problem #2

Calculate the force on the

4.0 C charge due to the other two

charges.60o 60o

+4 C

+1 C+1 C

Problem #3

Calculate the mass of ball B, which is suspended in midair.

A

B

q = 1.50 nC

q = -0.50 nC

R = 1.3 m

Problem #2Two 5.0 C positive point charges are 1.0 m apart.What is the magnitude and direction of the electric field at a point halfway between them?

Problem #4Calculate the magnitude of the charge on each ball, presuming they are equally charged.

A B

0.10 kg

1.0 m40o

1.0 m

0.10 kg