Coulomb´s Law & Gauss´s Law

Coulomb´s Law & Gauss´s Law Coulomb´s Law Discussion : Experimental Law Applicable to point charges only Gives Force between charges at rest and not for Charges in motion Coulomb interaction between charges is a long range force Follows Newton’s third Law Gives Force between charges at rest and not for charges in motion Coulomb interaction is long range force

Physics Paper CBSc I

Expression for force experienced by Test Charge:

Important Definitions • Source Charge : A point charge which exerts electrostatic force and produces an electric field. • Test Charge: A point charge which experiences electrostatic force and detectes an electric field. • Source point: Location of source charge. • Test point/ Observation point : Location of test charge.

Electric Field • The space around a charged body within which its influence can be felt/ The space around a charged body within which it exerts force on a test charge. • Electric Field Intensity: Electric Field Intensity at a point is force experienced per unit test charge at that point. • Unit: NC-1 or Vm-1 • Vector Quantity

Principle of Superposition of Electric Fields • The electric field at any point due to a set of fixed charges is equal to the vector sum of electric fields due to individual charges. • For discrete distribution of charge

For linear distribution of charge • For surface distribution of charge • For volume distribution of charge

Electric Dipole • A system consisting of two equal and opposite charges (–q and +q) separated by certain distance (2l) • Electric dipole moment Directed from negative to positive charge. • Monopole moment of electric dipole : Algebraic sum of charges and is equal to zero. p -q 2l +q

Electric Field Due to Dipole Located at origin • At point A on axial line Y P B(0,b,0) r p q X –q O l l +q A(a,0,0)

(b) At a point on equatorial line

(c) At arbitrary point Y P r p q X –q O l l +q

Electric Field due to Infinite Linear Distribution of Charge Y L(0,y,0) q R0 R (x,0,0) X + – 0 ldx

Electric Field Due to Uniformly Charged Ring z R ldl dq q y O P(x,0,0) x

Electric Field due to Uniformly Charged Circular Disc If  =surface charge density Electric field at P(x, 0,0) due to elementary ring z a dr r y O P(x,0,0) x

Electric Flux • The electric flux linked with an area is the number of electric force field lines crossing that area. • For uniform electric field • For non uniform electric field • Electric Flux may be + ve or – ve or zero • Outward Flux is + ve , Inward Flux is -ve

Gauss’s Law • The total electric flux through a closed surface is equal to times the charge enclosed by the surface when medium is vacuum. • If the closed surface encloses a no. of charges Where qnet is the net charge enclosed by the surface.

Differential form of Gauss’s Law • It relates the electric field at any point in space to the volume charge density ρ at same point. • It is a point equation. • It is one of the Maxwell’s equations for electricity and magnetism. • It can be used to find volume charge density at a given point if electric field intensity at that point is known.

Coulomb´s Law & Gauss´s Law