Batch VI: CH22B108-CH22B119 and EE22B001-EE22B073

Calendar

First  Instruction day: 13/03/2023, Last instruction day: 22/06/2023

Tentatively there will be 41 lectures and 10 tutorials. 

Quiz-I: 20/04/2023, Quiz-II: 25/05/2023, Endsem: 28/06/2023

Evaluation pattern: Quiz-I: 20 marks, Quiz-II:  20 marks, Endsem: 60 marks

Note: ASSIGNMENT 1 is already on moodle.

 THE PH1020-SHEET
1 q
E= r.̂ Electric field due to a point charge
4πϵ0 r 2
1⇢
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r ·· E
E== ⇢, r⇥E=0 ρ
✏✏0 ∇⋅E= Differential form
ϵ0
Maxwell’s equations for electrostatics
Qenc
∮
E ⋅ da = Integral form
Electrostatic potential, V, is defined as E =
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rV ϵ0
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2 ⇢
r V =
✏0
Poisson’s equation
Superposition principle E = Ei
∑
i
Continuous Charge Distributions

2
Potential energy of a discrete charge distribution Lets make a collection of 4 charges

First comes for free and second costs

While the third and fourth one cost

Total cost

In general, we have

Or, the potential energy stored in the system is

3
Potential energy of a continuous charge distribution

For a volume charge density, we have

Let the surface be at infinity

4
Potential energy of a charge distribution
Consistent?

Because electrostatic energy is quadratic in the

fields, it does not obey a superposition principle.

5
Conductors
A conductor in an
A perfect conductor contains unlimited supply of free charges electric field E0 induces
An ideal conductor does not exist but metals come very close charges on the surface.

E = 0 inside a conductor at the electrostatic equilibrium (when This leads to an electric

there is no net motion of charge within a conductor field E1 inside the
conductor.
Gauss’s law ∇ ⋅ E = ρ/ϵ0, implies that ρ = 0 inside a conductor
E1 and E0 cancel inside
Any charge resides on the surface of a conductor
but not outside

Electric field is perpendicular to the surface

b

∫a
A conductor is an equipotential:V(b) − V(a) = − E ⋅ dl =0

In summary, E = ρ = 0 inside an ideal conductor

6
Induced charges
Electric field of charge q will
induces charges on the conductor
due to the field it creates

This happens as the charge of

the conductor moves around in
such a way as to kill off the field
of q for points inside the
conductor, where the total field
must be zero.) A conductor with a cavity will
have electric field in the cavity
Charge enclosed by dotted surface
is zero and thus total charge on
outer surface is +q.

7
Boundary conditions

Gauss’s law

For a very thin pillbox

The normal component of E is discontinuous by an amount σ/ϵ0 at any boundary.

1
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r · E = ⇢, r⇥E=0
✏
Maxwell’s equation - zero curl

8
 Boundary conditions

What is the electric field outside a conductor with surface charge σ?

Because of Eq.(2.33) and the fact that the electric field inside a
conduction is zero, field just outside a conductor is

9
 Surface charge and the Force per unit area
In presence of electric field, surface charge will experience a force. Which
electric field to use in expression of force (above or below)?

It should just be f = σ Eother, which is..

What is the force per unit area

on a sheet of charge?

σ2
So for an ideal conductor, where field inside is zero, force per unit area: f = n̂
2ϵ0 10
12
13
Multipole expansion

14
Multipole expansion

15
Multipole expansion

the multipole expansion of V in powers of 1/r.

16
Multipole expansion

17
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Multipole expansion

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