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Short Notes of Electrostatics


Electrostatics: It is a branch of physics that deals with the phenomena
and properties of stationary or slow-moving electric charges with no
acceleration
...

F = Kq1q2/r2
Here, K = 1/4πε0 = 9×109 Nm2C-2 (in free space)



Relative Permittivity (εr):
The relative permittivity (εr) of a medium is defined as the ratio
between its permittivity of the medium (ε) and the permittivity (ε0) of
the free space
...
H
...

If q1q2<0, a negative sign from q1q2 will change
and
...



Unit of Charge:
C
...
S, q = ±1 stat-coulomb
S
...
m
...

So, εr = ε/ε0 = F1/F2

Here, F1 and F2 are the magnitudes of the force between them in free space
and in a medium respectively
...
The
direction of field is given by the direction of motion of a unit positive
charge if it were free to move
...
The direction of motion of
unit positive charge gives the direction of line of force
...

(b) A line of force starts from a positive charge and ends on a negative
charge
...



Electric field intensity due to a point charge: E = (1/4πε0) (q/r2)



Electric field Intensity due to a linear distribution of charge:

(a) At point on its axis
...

(b) At a point on the line perpendicular to one end
...



Electric field due to ring of uniform charge distribution:

At a point on its axis, E = (1/4πε0) [qx/(a2+x2)3/2]


Electric field due to uniformly charged disc:

Here σ is the surface charge
...




Dipole Moment:- Dipole moment ( ) of an electric dipole is defined
as the product of the magnitude of one of the charges and the vector
distance from negative to positive charge
...
I), stat coulomb cm (non
S
...


(b) At a point on the equatorial line (perpendicular bisector):-

(c) At any point:-



Torque ( ) acting on a electric dipole in a uniform electric field
(E):= pE sinθ
Here, p is the dipole moment and θ is the angle between direction of
dipole moment and electric field E
...




Gauss Theorem:- It states that, for any distribution of charges, the
total electric flux linked with a closed surface is 1/ε0 times the total
charge with in the surface
...



Electric field of a spherically symmetric distribution of charge of
Radius R:-

(a) Point at outside (r > R):- E = (1/4πε0) (q/r2), Here q is the total
charge
...



Electric field due to an infinite non-conducting flat sheet having
charge σ:E = σ/2ε0

This signifies, the electric field near a charged sheet is independent of
the distance of the point from the sheet and depends only upon its charge
density and is directed normally to the sheet
...


(b) V(r) = kq/r
(c) Potential difference, between any two points, in an electric field is
defined as the work done in taking a unit positive charge from one point to the
other against the electric field
...
I), stat-volt (C
...
S)
Dimension:- [V] = [ML2T-3A-1]
Relation between volt and stat-volt:- 1 volt = (1/300) stat-volt


Relation between electric field (E) and electric potential (V):E = -dV/dx = --dV/dr



Potential due to a point charge:V = (1/4π ε0) (q/r)



Potential at point due to several charges:V = (1/4π ε0) [q1/r1 + q2/r2 + q3/r3]
= V1+V2+ V2+…
...


(a) If θ = 90º, then W = 0
(b) If θ = 0º, then W = -pE
(c) If θ = 180º, then W = pE


Kinetic energy of a charged particle moving through a potential
difference:K
...




Insulators:- Insulators (also called dielectrics) are those substances
through which electric charge cannot pass easily
...
I – farad (coulomb/volt)
C
...
S – stat farad (stat-coulomb/stat-volt)
Dimension of C:- [M-1L-2T4A2]



Capacity of an isolated spherical conductor:C = 4πε0r



Capacitor:- A capacitor or a condenser is an arrangement which
provides a larger capacity in a smaller space
...



Effect of dielectric on the capacitance of a capacitor:C = ε0A/[d-t+(t/K)]

Here d is the separation between the plates, t is the thickness of the
dielectric slab A is the area and K is the dielectric constant of the material
of the slab
...



Capacity of a cylindrical condenser:Cair = λl / [(λ/2π ε0) (loge b/a)] = [2π ε0l /(loge b/a) ]
Cmed = [2πKε0l /(loge b/a) ]



Potential energy of a charged capacitor (Energy stored in a
capacitor):W = ½ QV = ½ Q2/C = ½ CV2



Energy density of a capacitor:U = ½ ε0E2 = ½ (σ2/ ε0)
This signifies the energy density of a capacitor is independent of the area
of plates of distance between them so long the value of E does not change
...
+Cn

The resultant capacity of a number of capacitors, connected
in parallel, is equal to the sum of their individual capacities
...

(ii) q1 = q2 = q3 = q
(iii) V1= q/C1, V2= q/C2, V3= q/C3
(iv) Energy Stored, U = U1+U2+U3


Energy stored in a group of capacitors:(a) Energy stored in a series combination of capacitors:-

W = ½ (q2/C1) + ½ (q2/C2) + ½ (q2/C3) = W1+W2+W3
Thus, net energy stored in the combination is equal to the sum of the
energies stored in the component capacitors
...



Force of attraction between plates of a charged capacitor:(a) F = ½ ε0E2A
(b) F = σ2A/2ε0
(c) F=Q2/2ε0A



Force on a dielectric in a capacitor:F = (Q2/2C2) (dC/dx) = ½ V2 (dC/dx)



Common potential when two capacitors are connected:V = [C1V1+ C2V2] / [C1+C2] = [Q1+Q2]/ [C1+C2]



Charge transfer when two capacitors are connected:ΔQ = [C1C2/C1+C2] [V1-V2]



Energy loss when two capacitors are connected:ΔU = ½ [C1C2/C1+C2] [V1-V2] 2



Charging of a capacitor:(a) Q = Q0(1-e-t/RC)
(b) V = V0(1-e-t/RC)
(c) I = I0(1-e-t/RC)
(d) I0 = V0/R



Discharging of a capacitor:(a) Q = Q0(e-t/RC)
(b) V = V0(e-t/RC)
(c) I = I0(e-t/RC)



Time constant:-



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