Fall 2004

Coulomb’s Law

ECE 2317: Applied Electricity and Magnetism

Prof. Valery KalatskyDept. of Electrical & Computer Engineering

University of Houston

Title

Electric charge

Electric Charge

A basic law of the universe is that like charges repel and unlike attract.

Two negatives will repel each other.

A negative and a positive will attract each other.

Today’s lecture:

Quantitative description of forces between electric charges

Electric Forces: basics

Electric Forces: basics

Electric forces act between charges

An electric charge DOES NOT exert a force upon itself

Attraction

Repulsion

Electric forces depend on the amount of charge

Larger separation makes force smaller

Electric forces depend on the distance between charges

Larger charges produces larger force

Electric Forces: Coulomb’s Law

Electric Forces: Coulomb’s Law

0 = 8.854×10-12 [C2/(N m2)]Permittivity of free space

Coulomb’s Law: vectors

q1 (x1,y1,z1)

x

y

zR

r1

r2

q2 (x2,y2,z2)

aR

Coulomb’s Law: Vectors

aR = RR

4R2F =

q1 q2 [N]aR

, R = r1 - r2

Coulomb Charles-Augustin de Coulomb

French engineer & physicist best known for the formulation of Coulomb's law. Invented torsion balance to measure the electric forces.

Torsion Balance

Torsion Balance

Example

q1=0.7 [mC] located at (3,5,7) [m]

q2=4.9 [C] located at (1,2,1) [m]

Find: F1, F2

F1 = force on charge q1

F2 = force on charge q2

Example

Multiple charges

Multiple Charges

Principle of superposition

Electric Field

Electric Field

4R2E =

q1 [N/C] or [V/m]aR

x

y

zR

r2

r1

q1 q2

q2

E =F2

aR = RR

4R2F =

q1 q2 [N]aR

, R = r2 – r1

Electric Field is the force acting on a 1[C] charge

Electric Field: Multiple Charges

Electric Field: Multiple Charges

x

y

zq1 @ r1

q2

q1

R1

R2 RNR3

q3 qN

q2 @ r2

...

qN @ rN

R1 = r - r1

R2 = r - r2

...

RN = r - rN

E=E1+E2+…+EN (superposition)

r

E =4R1

2

q1 aR1 +

4R22

q2 aR2 +

4R32

q3 aR3 + …

Electric Field: Charge Distribution

Electric Field: Charge Distribution

x

y

zr = (x,y,z)

V (r´) = V (x´,y´,z´)

R

r´(x´,y´,z´)

Electric Field: Charge Distribution

x

y

z r = (x,y,z)

R

dQ = V (r´) dV´

dV´r´(x´,y´,z´)

Electric Field: Charge Distribution

4R2dE =

dQaR

4R2dE =

V (r´ )aR dV´

V

t

t

t

t