Fall 2004 Coulomb’s Law ECE 2317: Applied Electricity and Magnetism Prof. Valery Kalatsky Dept. of Electrical & Computer Engineering University of Houston TitleTitle

Electric chargeElectric 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: basicsElectric 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 LawElectric Forces: Coulomb’s Law Electric Forces: Coulomb’s Law  0 = 8.854× [C 2 /(N m 2 )] Permittivity of free space

Coulomb’s Law: vectorsCoulomb’s Law: vectors q 1 (x 1,y 1,z 1 ) x y z R r1r1 r2r2 q 2 (x 2,y 2,z 2 ) aRaR Coulomb’s Law: Vectors a R = R R 4    R 2 F = q 1 q 2 [N] aRaR, R = r 1 - r 2

CoulombCoulomb 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 BalanceTorsion Balance Torsion Balance

ExampleExample q 1 =0.7 [mC] located at (3,5,7) [m] q 2 =4.9 [  C] located at (1,2,1) [m] Find: F 1, F 2 F 1 = force on charge q 1 F 2 = force on charge q 2 Example

Multiple chargesMultiple charges Multiple Charges Principle of superposition

Electric FieldElectric Field Electric Field 4    R 2 E = q1q1 [N/C] or [V/m] aRaR x y z R r2r2 r1r1 q1q1 q2q2 q2q2 E = F2F2 a R = R R 4    R 2 F = q 1 q 2 [N] aRaR, R = r 2 – r 1 Electric Field is the force acting on a 1[C] charge

Electric Field: Multiple ChargesElectric Field: Multiple Charges Electric Field: Multiple Charges x y z q r 1 q2q2 q1q1 R1R1 R2R2 RNRN R3R3 q3q3 qNqN q r 2... q r N R 1 = r - r 1 R 2 = r - r 2... R N = r - r N E=E 1 +E 2 +…+E N (superposition) r E = 4    R 1 2 q1q1 a R    R 2 2 q2q2 a R    R 3 2 q3q3 a R 3 + …

Electric Field: Charge DistributionElectric Field: Charge Distribution Electric Field: Charge Distribution x y z r = (x,y,z)  V (r´) =  V (x´,y´,z´) R r ´ (x ´,y ´,z ´ )

Electric Field: Charge DistributionElectric Field: Charge Distribution x y z r = (x,y,z) R dQ =  V (r´) dV´ dV´ r ´ (x ´,y ´,z ´ ) Electric Field: Charge Distribution 4    R 2 dE = dQ aRaR 4    R 2 dE =  V (r´ ) a R dV ´ V 

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