Coulomb´s Law & Gauss´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 C BSc 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 surface 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 l O l +q A(a,0,0)

(b) At a point on equatorial line

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

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

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

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

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.