NCERT Solution Class 12th Physics Chapter – 2 Electrostatic Potential and Capacitance Notes

NCERT Solution Class 12th Physics Chapter – 2 Electrostatic Potential and Capacitance

NCERT Solution Class 12th Physics Chapter – 2 Electrostatic Potential and Capacitance

?Chapter – 2?

✍Electrostatic Potential and Capacitance✍

?Notes?

The S.I. unit of electric potential and a potential difference is volt.

1 V = 1 J C^-1.

Electric potential due to a + ve source charge is + ve and – ve due to a – ve charge.

The change in potential per unit distance is called a potential gradient.

The electric potential at a point on the equatorial line of an electric dipole is zero.

Potential is the same at every point of the equipotential surface.

The electric potential of the earth is arbitrarily assumed to be zero.

Electric potential is a scalar quantity.

The electric potential inside the charged conductor is the same as that on its surface. This is true irrespective of the shape of the conductor.

The surface of a charged conductor is equipotential irrespective of its shape.

The potential of a conductor varies directly as the charge on it. i.e., V ∝ l/A

Potential varies inversely as the area of the charged conductor i.e.

S.I. unit of capacitance is Farad (F).

The aspherical capacitor consists of two concentric spheres.

A cylindrical capacitor consists of two co-axial cylinders.

Series combination is useful when a single capacitor is not able to tolerate a high potential drop.

Work done in moving a test charge around a closed path is always zero.

The equivalent capacitance of series combination of n capacitors each of capacitance C is
C_s = C/n

C_s is lesser than the least capacitance in the series combination.

The parallel combination is useful when we require large capacitance and a large charge is accumulated on the combination.

If two charged conductors are connected to each other, then energy is lost due to sharing of charges, unless initially, both the conductors are at the same potentials.

The capacitance of the capacitor increases with the dielectric constant of the medium between the plates.

The charge on each capacitor remains the same but the potential difference is different when the capacitors are connected in series.

P. D. across each capacitor remains the same but the charge stored across each is different during the parallel combination of capacitors.

P.E. of the electric dipole is minimum when θ = 0 and maximum when θ = 180°

θ = 0° corresponds to the position of stable equilibrium and θ = π to the position of unstable equilibrium.

The energy supplied by a battery to a capacitor is CE² but energy stored in the capacitor is 1/2 CE².

A suitable material for use as a dielectric in a capacitor must have a high dielectric constant and high dielectric strength.

Van-de Graaf generator works on the principle of electrostatic. induction and action of sharp points on a charged conductor.

The potential difference between the two points is said to be 1 V if 1 J of work is done in moving 1 C test charge from one point to the another.

The electric potential at a point inIt is defined as the amount of work done in moving a unit + ve test charge front infinity to that point.

Electric potential energy – It is defined as the amount of work is done in bringing the charges constituting a system from infinity to their respective locations.

1 Farad – The capacitance of a capacitor is said to be 1 Farad if 1 C charge given to it raises its potential by 1 V

Dielectric – It is defined as an insulator that doesn’t conduct electricity but the induced charges are produced on its faces when placed in a uniform electric field.

Dielectric Constant – It is defined as the ratio of the capacitance of the capacitor with a medium between the plates to its capacitance with air between the plates

Polarisation – It is defined as the induced dipole moment per unit volume of the dielectric slab.

The energy density of the parallel plate capacitor is defined as the energy per unit volume of the capacitor.

Electrical Capacitance – It is defined as the ability of the conductor to store electric charge.

Important Formulae

Electric potential at a point A is
V_A = W∞A/q0

V = 1/4πε₀.q/r

Electric field is related to potential gradient as:
E = – dV/dr

Electric potential at point on the axial line of an electric dipole is:
V = 1/4πε₀⋅qr²

Electric P.E. of a system of point charges is given

V due to a charged circular ring on its axis is given by:
V = 1/4πε₀⋅q / (R2+r2)^1/2

V at the centre of ring of radius R is given by
V =  1/4πε₀⋅q / R

The work done in moviag a test large from one point A to another point B having positions vectors rA→ and rA→ respectively w.r.t. q is given by
WAB =  1/4πε₀⋅q⋅(1/rB − 1/rA)

Line integral of electric field between points A and B is given by.

Electric potential energy of an electric dipole is

Capacitance of the capacitor is given by
C = q / V

P.E. of a charged capacitor is:

C of a parallel plate capacitor with air between the plates is:
C₀ = ε0⋅A / d
C₀ = ε0KA / d

C of a parallel plate capacitor with a dielectric medium between the plates is:
C = Cm / C0 = E₀ / E

Common potential as
V = C₁V₁ + C₂V₂ / C₁+C₂

loss of electrical energy =

Energy supplied by battery is CE2 and energy stored in the capacitor is 1/2 CE².

The equivalent capacitance of series combination of three capacitor is given by
1C_s = 1/C₁ + 1/C₂ + 1/C₃

The equivalent capacitance of parallel grouping of three capacitors is
C_p = C₁ + C₂ + C₃

Capacitance of spherical capacitor is
C = 4πε₀ ab/b−a
a, b are radii of inner and outer spheres.

Capacitance of a cylindrical capacitor is given by:

when b, a are radii of outer and inner cylinder.

Capacitance of a capacitor in presence of conducting slab between the plates is .

Capacitances of a capacitor with a dielectric medium between the plates is given by

Reduced value of electric field in a dielectric slab is given by
E = E₀ – P/ε₀
where P = σ_p = induced charge density.

Capacitance of an isolated sphere is given by
C = 4πε₀ r .
C = 4πε₀ Kr