Revision: Class 12 >> Electrostatic Potential and Capacitance NEET (UG) Electrostatic Potential and Capacitance

The work done by an external force in bringing a unit positive charge from infinity to that point is called electric potential at that point.

The work done against the electrostatic forces to achieve a certain configuration of charges in a given system is called electrostatic potential energy.

"Potential difference is the work done to move a unit charge from one point to another in an electric field."

OR

The difference in electric potential between two points B and A, given by ΔV = V_B − V_A = \[\frac {W_AB}{q_0}\]​​, is called potential difference.

Conductors are those through which electric charge can easily flow. Metals, human body, earth, mercury and electrolytes are conductors of electricity.

OR

Substances which offer high resistance to the passage of electricity and do not allow electricity to pass through them easily, are called insulators.

OR

The material through which electric charge can flow easily is called a conductor.

Substances whose resistance to the movement of charges is intermediate between conductors and insulators, are called semiconductors.

Those substances in which electric charge cannot flow are called ‘insulators' (or dielectrics). Glass, hard-rubber, plastics and dry wood are insulators. Insulators have practically no free electrons.

OR

The material in which electrons are tightly bound to the nucleus and thus not available for conductance is called an insulator.

The surface at which electric potential is the same at each point is called an equipotential surface.

The phenomenon in which the electric field inside a cavity of a conductor is zero, irrespective of external charges or fields, is called electrostatic shielding.

Non-conducting substances which cannot transmit electric charge through them are called dielectrics.

The molecule in which the centres of positive and negative charges are separated even when there is no external field, and which has a permanent dipole moment, is called a polar molecule. (e.g. HCl, H₂O, alcohol, NH₃)

The molecule in which the centres of positive and negative charges coincide and which has no permanent dipole moment in its normal state is called a non-polar molecule. (e.g. O₂, H₂, N₂, CO₂, benzene, methane)

A dielectric that has a permanent electric dipole moment even if the external electric field is absent is called a polar dielectric.

A dielectric in which every molecule has zero dipole moment in its normal state is called a non-polar dielectric.

Alignment of dipole moments (permanent or induced) in the direction of an applied electric field is called polarisation.

A system consisting of two conductors having equal and opposite charges separated by an insulator or dielectric is called a capacitor.

The maximum electric field that a dielectric medium can withstand without breakdown (of its insulating property) is called its dielectric strength.

The ratio of the charge Q given to one of the conductors of a capacitor to the potential difference V between the conductors is called its capacitance, given by C = Q/V.

The ability of a conductor to store charge is called the capacity of conductor.

A capacitor that consists of two large, parallel, conducting plates separated by a small distance is called a parallel plate capacitor.

The ratio of the permittivity of a medium to the permittivity of vacuum.

K = ε / ε₀

OR

Dielectric constant is the factor by which the capacitance of a capacitor increases when a dielectric is completely inserted between its plates.

The product of vacuum permittivity and dielectric constant of the medium.

ε = ε₀K

Potential difference (V) between two points = Work done (W)/Charge (Q)
V = \[\frac {W}{Q}\]

The SI unit of electric potential difference is volt (V)

1 volt = \[\frac{1\mathrm{~joule}}{1\mathrm{~coulomb}}\] = 1 J C^-1

\[V=\frac{Q}{4\pi\varepsilon_0r}\]

Potential due to System of Charges:

\[U=\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r_{12}}\]

U = \[\frac{1}{4\pi\varepsilon_0}\cdot\frac{q_1q_2}{r_{12}}\]

V = \[\frac{1}{4\pi\varepsilon_0}\cdot\frac{q}{r}\]

Varies on spherical shell carrying charge q and radius R:

• Inside shell (r < R): V = \[\frac {1}{4πε_0}\] ⋅ \[\frac {q}{R}\]
• On surface (r = R): V = \[\frac {1}{4πε_0}\] ⋅ \[\frac {q}{R}\]
• Outside shell (r > R): V = \[\frac {1}{4πε_0}\] ⋅ \[\frac {q}{r}\]

\[V=\frac{1}{4\pi\varepsilon_{0}}\cdot\frac{p\cos\theta}{r^{2}}=\frac{1}{4\pi\varepsilon_{0}}\cdot\frac{\vec{p}\cdot\vec{r}}{r^{3}}(r>>a)\]

\[V=\frac{1}{4\pi\varepsilon_{0}}\left[\frac{q_{1}}{r_{1}}+\frac{q_{2}}{r_{2}}+\frac{q_{2}}{r_{3}}+\frac{q_{4}}{r_{4}}+.........+\frac{q_{n}}{r_{n}}\right]\]

\[V=\frac{1}{4\pi\varepsilon_0}\sum_{i=1}^{i=n}\frac{q_i}{r_i}\]

\[\vec{E}=\frac{\sigma}{\varepsilon_0}\hat{n}\]

where
σ = surface charge density
\[\hat n\] = outward normal unit vector

Magnitude form:

E = \[\frac{\sigma}{\varepsilon_0}\]

Defined as dipole moment per unit volume:

\[P=\frac{\text{dipole moment}}{\mathrm{volume}}=np\]

C = \[\frac {2πkε₀ l}{2.303 log(b/a)}\]

C = 4πkε₀ · [\[\frac {ab}{(b − a)}\]]

C = Q/V

For two plates separated by distance d:

\[C=\frac{\varepsilon_0A}{d}\]

With a dielectric medium:

\[C=\frac{K\varepsilon_0A}{d}\]

W = \[\frac {1}{2}\]qV

Capacitors in Series:

Equivalent capacitance: \[\frac{1}{C_s}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\cdots\]

• Same voltage (V) across all capacitors
• Charge divides
• The equivalent capacitance is greater than the largest capacitor

Capacitors in Parallel:

\[C_p=C_1+C_2+C_3+\cdots\]

• Same voltage (V) across all capacitors
• Charge divides
• The equivalent capacitance is greater than the largest capacitor