Chapter 2 Electrostatic Potential and Capacitance  | class 12th | quick revision notes physics

Ch-2 Electrostatic Potential and Capacitance Class 12 Physics Hand ritten Notes By Ashish Anand Sir

Electrostatic Potential and Capacitance Notes Class 12 Physics Chapter 2

→ 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 ∝ lA

→ 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 = Cn

→ 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 12 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 in E→: It 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∞Aq0

→ V = 14πε0.qr

→ Electric field is related to potential gradient as:
E = – dVdr

→Electric potential at point on the axial line of an electric dipole is:
V = 14πε0⋅qr2

→ Electric P.E. of a system of point charges is given
υ = 14πε0∑ni=1∑nj=1j≠iqiajrij

→ V due to a charged circular ring on its axis is given by:
V = 14πε0⋅q(R2+r2)1/2

→ V at the centre of ring of radius R is given by
V = 14πε0⋅qR

→ 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 = 14πε0⋅q⋅(1rB−1rA)

→ Line integral of electric field between points A and B is given by.
∫AB E→ dl→ = 14πε0⋅q(1rA−1rB)

→ Electric potential energy of an electric dipole is
U = – p→. E→

→ Capacitance of the capacitor is given by
C = qV

→ P.E. of a charged capacitor is:
U = 12 qV = 12 CV² = q22C

→ C of a parallel plate capacitor with air between the plates is:
C₀ = ε0⋅Ad
C₀ = ε0KAd

→ C of a parallel plate capacitor with a dielectric medium between the plates is:
C = CmC0=E0E

→ Common potential as
V = C1V1+C2V2C1+C2

→ loss of electrical energy = 12(C1C2C1+C2)(V1−V2)

→ Energy supplied by battery is CE2 and energy stored in the capacitor is 12 CE².

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

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

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

→ Capacitance of a cylindrical capacitor is given by:
C = 2πε0loge(ba)
when b, a are radii of outer and inner cylinder.

→ Capacitance of a capacitor in presence of conducting slab between the plates is .
C = C01−td = ∞ if t = d.

→Capacitances of a capacitor with a dielectric medium between the plates is given by
C = C0[1−td(1−1R)]
C = K C₀ If t = d

→ Reduced value of electric field in a dielectric slab is given by
E = E₀ – Pε0
where P = σ_p = induced charge density.

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