fall 2004 coulomb’s law ece 2317: applied electricity and magnetism prof. valery kalatsky dept. of...
TRANSCRIPT
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