Electrostatics

Charge
Charge is quantized.

Q = ne

Law of Conservation of Charge = Charge can neither be created nor be destroyed, it can only be transferred from one body to another.

Coulomb's Law
When two charges, touch each other , the charge is equally shared by them. The electrostatic force inside a conductor is zero.

F = k q1q2 / r2

where k = 1 / 4πε = 9 x 109Nm2/C2

Charge Density
λ = Q/l

σ = Q/A

ρ = Q/V

Dipole Moment
p = Q.2l

Torque
Torque = pEsinθ

Electric Field Intensity
E = F/Q

E = k q / r2(due to point charge)

Due to Dipole : E = k psinθ / r3

Inside a Conductor : k = infinite ... E = 0

Note : Potential decreases in the direction of Electric Field Intensity.

Due to Conductor of length L and at distance a :

E = k q / r  [1/a - 1/(L+a)]

Non-Conducting Sphere :

The Electric Field Intnsity inside and outsid a non-conductor aries just like g varies wih depth and height.

Electric Lines of Force

 * 1) No two electric lines of force can intersect each other, they are always parallel.
 * 2) Electric Lines of Force are close continuous curves and they start from positive and end on negative charge.
 * 3) The tangent drawn at any instant to the lines of force, gives it direction at that instant.
 * 4) The lines are more crowded where the field is strong and less crowded where the field is weak.
 * 5) When two unlike charges are placed close to each other, the lines of force are compressed ; this explains attraction of unlike charges.
 * 6) When two like charges are placed close to each other, the lines of force exert lateral pressure on each other , this explains repulsion of like charges.

Electric Potential Energy
U = F.r = k q1q2/r

Potential Energy of System of Charges :

U = U1 + U2 + U3 +.......+ Un

Potential Energy of Dipole in an External Field :

U = -pEcosθ

Wor done in rotating a dipole from θ1 to θ2= - pE (cosθ1 - cos θ2)

Electric Potential
V = U/q = F.r / q = k q/r

V = Er = U/Q

... U = VQ

The sign of Potential depends on like/unlike charges.

Cases of Potential :
 * 1) Due to point charge :  V = - kq/r  ... at r = 0, Z is negative infinite . The graph will be negative , curved and parallel to V and r axes.
 * 2) Inside a Solid Sphere : V = - kq (1.5R2 - 0.5r2) / R3. At r=R ,V = - kq/R . At r = 0 ,V = -1.5kq/R  The graph is negative, parabolic.
 * 3) Outside a Solid Sphere : V = -kq/r, at r = infinity , V = 0 ; On surface , V = -kq/R
 * 4) Due to a Spherical Shell : Outside  V = -kq/r . Inside V = - kq/r
 * 5) On the Axis of a Ring : V = - kq / sqrt(R2+x2)

Due to Dipole : V = k pcosθ / r2

At an equatorial point, the electric potential is zero

Note : Potential decreases in the direction of Electric Field Intensity.

Common Potential
Suppose two spheres of radii r1 & r2 are connected by a wire and charges q1& q2 are residing on their surfaces

then Common Potential = [q1 + q2] / 4πε(r1+r2)

Potential Difference
VAB = VA - VB

Electric Flux
Φ = Edscosθ

Gauss' Theorem
NEI = εE

TNEI = ∫ NEI = ∫ εE dscosθ

The Gauss's Law states that the Total Normal Electric Induction is equal to the algebraic sum of the Charges enclosed by the surface.

TNEI = Qi

Applications of Gauss's Law

 * 1) Sphere : E = 1 / 4πε0  q/r2
 * 2) Cylinder : E = λ/2πε0r
 * 3) Any Shape : E = σ / ε0
 * 4) Sheet : E = σ /2 ε0

Mechanical Force
Mechanical Force per Unit Area = 1/2 E2ε = 1/2 σ2/ε

Energy Density
Potential Energy per unit Volume = 1/2 E2ε = 1/2 σ2/ε

Dielectrics and Polarization
Polar

Non-Polar

Electric Moments

Polarization = P = σp  {Amount of charge induced due to external electric field}

Capacitance
Q = CV

C = Q/V

C = Aε / d

Series Combination :

Cs = 1/C1 + 1/C2 + 1/C3 + .... +1/Cn

Parallel Combination :

Cp = C1 + C2 + C3 + .... + Cn

Energy Stored in a Capacitor :

E = 1/2 CV2

Force between the plates of Capacitor :

F = Q2 / 2Aε

C = kCo

Tips and Tricks
1) For repulsive force between two like charges, the closest distance of approach is when Kinetic Energy is equal to Potential Energy.

2) For questions related to Flux and Electric Field Intensity, consider Gauss Theorem.

The formulae for E, at diffrent distances from a conductor , circuar conductor and at centre of circular conductor is the sam as B.