- Electric potential is a scalar quantity, and it is positive near a positive charge and negative near a negative charge.
- Electric potential is taken as zero at infinity because the force between charges becomes zero at infinite separation.
- The potential difference between two points is measured using a voltmeter, which is connected in parallel with the circuit, with its positive terminal at the higher-potential point.
Definitions [31]
Definition: Electric Potential
Electric Potential (V) at a point in an electric field is defined as the work done per unit positive charge in bringing a small test charge from infinity to that point, without acceleration.
Define Electric potential.
Electric potential is a measure of work done on the unit's positive charge to bring it to that point against all electrical forces. It is represented as ‘V’.
Define the following:
Potential difference
Potential difference: The potential difference between two points may be defined as the work done in moving a unit positive charge from one point to the other.
Definition: Potential Difference
The potential difference (p.d.) between two points is equal to the work done per unit charge in moving a positive test charge from one point to the other.
OR
The work done per unit positive charge in moving a charge from one point to another in an electric field is called the potential difference between those two points.
OR
The potential difference between any two points in the circuit is the amount of energy needed to move one unit of electric charge from one point to the other.
Definition: Work Done in Moving a Charge
Work done in moving a charge in an electrostatic field is the energy transferred when a charge q is displaced between two points having a potential difference VA − VB.
Definition: Electric Potential Due to a Point Charge
The work done by an external agent in bringing a unit positive test charge slowly from infinity to a point in an electric field, against the electrostatic force, is called the electric potential at that point.
Definition: Potential Gradient
Potential Gradient is the rate of change of electric potential (V) with respect to distance (r) in the direction of the electric field.
Definition: Equipotential Surface
The surface at which electric potential is the same at each point is called an equipotential surface.
OR
Any surface over which the electric potential is the same everywhere is called an equipotential surface.
Definition: Electric Potential Energy of a System of Charges
The total work done in bringing all the charges of the system from infinite separation to their present positions, without any change in kinetic energy.
Definition: Electrostatic Equilibrium Between Plates
A condition in which a charged body remains stationary between two parallel plates because the upward electric force exactly balances the downward gravitational force.
Definition: Electrostatic Potential Energy of a Dipole
The potential energy of an electric dipole in an electrostatic field is the amount of work done in bringing the dipole from infinity (or a reference position) into the field, or the work required to rotate it against the torque exerted by the field.
Definition: Electrostatic Equilibrium
The condition in which charges in a conductor are at rest, and no further motion of charges occurs.
Definition: Equipotential Body
A conductor in electrostatic equilibrium is an equipotential body, meaning all points on it are at the same electric potential.
Definition: Electrostatic Shielding
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.
Definition: Surface Charge Density
Surface charge density is the charge per unit area on the surface of a conductor and is denoted by \[\sigma\].
Definition: Free Charges
Charges that are loosely bound to atoms/molecules and can move freely through a material when an external electric field is applied.
Example: conduction electrons in metals, ions in electrolytes.
Definition: Bound Charges
Charges that are tightly bound to atoms/molecules and cannot migrate through the material. They can only undergo small displacement or realignment, producing polarisation.
Example: electrons bound to atomic nuclei in a dielectric.
Definition: Dielectric
A dielectric is a non-conducting substance in which, on the application of an external electric field, induced charges appear that oppose (but do not cancel) the applied field.
Definition: Polar Molecule
A molecule in which the centres of positive and negative charge do not coincide, giving it a permanent dipole moment even without an external field (e.g., H₂O, HCl, NH₃).
Definition: Non-Polar Molecule
A molecule in which the centres of positive and negative charge coincide, so the net dipole moment is zero in the absence of an external field (e.g., N₂, O₂, CO₂).
Definition: Polar Dielectric
A dielectric made of polar molecules; in the absence of a field, molecular dipoles are randomly oriented, giving zero net dipole moment overall.
Definition: Non-Polar Dielectric
A dielectric made of non-polar molecules; an external field induces a temporary dipole moment in each molecule, aligned with the field.
Definition: Dielectric Constant (K)
Dielectric Constant (K) is the ratio of the applied field to the net field inside the dielectric, indicating how much the material reduces the electric field.
Definition: Electric Polarisation
Electric Polarisation is the phenomenon in which an external electric field induces or aligns molecular dipoles within a dielectric, producing equal and opposite bound surface charges on its faces.
Definition: Dielectric Strength
Dielectric Strength is the maximum electric field a dielectric can withstand without electrical breakdown (i.e., before it starts conducting).
Definition: Capacitance
Capacitance is the ability of a conductor to store electric charge.
When charge q is given to an isolated conductor, its potential V rises. Experimentally, q is directly proportional to V:
q ∝ V ⟹ q = CV
where C is a constant called the capacitance of the conductor.
Definition: Capacitor
A capacitor is a device that stores electrical energy in the form of an electric field. It has two conducting plates separated by an insulating material called a dielectric (air, ceramic, mica, paper, or electrolyte).
Definition: The Parallel Plate Capacitor
A capacitor that consists of two large, parallel, conducting plates separated by a small distance is called a parallel plate capacitor.
Definition: Potential Difference (V)
The work done per unit charge in moving a charge from one plate of a capacitor to the other is called the potential difference between the plates.
Definition: Equivalent Capacitance
The capacitance of a single capacitor that stores the same charge at the same voltage as the entire combination is called the equivalent capacitance of the combination.
Definition: Energy Stored in a Capacitor
The work done in the transfer of charge q between the two plates of a capacitor, which gets stored in the form of potential energy of the system, is called the energy stored in a capacitor.
Formulae [21]
Formula: Electric Potential
V = \[\frac {W}{q}\]
- SI Unit: volt (V), where 1 V = 1 J/C
- Dimensional Formula: [M1L2T−3A−1]
- Nature: Scalar quantity (no direction, only magnitude)
Formula: Potential Due to a Point Charge
V = \[\frac{1}{4\pi\varepsilon_0}\frac{qr}{R^3}=\frac{\rho r}{3\varepsilon_0}\]
where k = 9 × 109 N m2/C2, q is the source charge, and r is the distance from the charge.
Formula: Potential Difference between A and B
\[V_A-V_B=\frac{W}{Q}\]
Formula: Work Done in Moving a Charge
W = q(VA − VB)
Where:
- W = work done (joules)
- q = magnitude of charge (coulombs)
- VA, VB = electric potentials at points A and B (volts), with A at higher potential
Formula: Electric Potential due to a Point Charge
\[V(r)=\frac{1}{4\pi\varepsilon_0K}\frac{q}{r}\]
- V(r) = electric potential at distance rr from the charge
- q = source charge
- ε0 = permittivity of free space
- K = dielectric constant of medium
- Reference is taken such that V(∞) = 0.
Fromula: Potential Gradient
Potential Gradient = V = \[\frac {dV}{dr}\]
- SI unit: V/m (vector quantity).
Formula: Work Done on an Equipotential Surface
When a charge q0 is moved from point A to point B on the same equipotential surface:
W = q0(VA − VB)
Since VA = VB on the surface:
W = 0
Formula: Potential Energy of Two Point Charges
U = \[\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r}\]
| Symbol | Meaning | Unit |
|---|---|---|
| U | Potential energy of the system | joule (J) |
| q1,q2 | Point charges | coulomb (C) |
| r | Distance between charges | metre (m) |
| ε0 | Permittivity of free space | 8.85 × 10−12 C2 N−1 m−2 |
Formula: Electric Field on a Charged Conductor Surface
\[\vec{E}=\frac{\sigma}{\varepsilon_0}\hat{n}\]
where
- σ = surface charge density
- \[\hat n\] = outward normal unit vector
- \[\varepsilon_0\] = permittivity of free space.
Magnitude form:
E = \[\frac{\sigma}{\varepsilon_0}\]
Vector form:
\[\vec{E} = \frac{\sigma}{\varepsilon_0}\hat{n}\]
Formula: Net Field Inside Dielectric
E = E0 − Einduced
Formula: Dielectric constant
Dielectric constant (relative permittivity):
K = \[\frac {ε}{ε_0}\]
where ε is the permittivity of the medium and ε0 is the permittivity of free space.
It can also be expressed as:
K = \[\frac {E_0}{E}\]
where E0 is the field without dielectric and E is the reduced field with dielectric inserted.
Formula: Dielectric Strength
Eds = \[\frac {V_{max}}{d}\]
SI unit: V/m
Formula: Dielectric Constant
K = \[\frac {E_0}{E}\]
K = \[\frac {\sigma}{\sigma-\sigma_i}\]
where σ = surface charge density on plates, σi = induced (bound) charge density.
Formula: Capacitance
C = \[\frac {q}{V}\]
Capacitance is the charge required to raise the potential of a conductor by one unit (1 volt).
Formula: Charge Stored
q = CV
Formula: Energy Stored
U = \[\frac {1}{2}\]CV2 (also U = Q2/2C or \[\frac {1}{2}\]QV)
Formula: Capacitance of a Parallel Plate Capacitor
For two plates separated by distance d:
\[C=\frac{\varepsilon_0A}{d}\]
With a dielectric medium:
\[C=\frac{K\varepsilon_0A}{d}\]
Formula: Series Combination
\[{\frac{1}{C_S}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\cdots}\]
For n identical capacitors of capacitance C each: CS = \[\frac {C}{n}\]
Formula: Voltage Distribution (Special Formula)
For two capacitors in series, the voltage across each is:
\[V_1=\frac{C_2}{C_1+C_2}\cdot V\]
\[V_2=\frac{C_1}{C_1+C_2}\cdot V\]
Physical Insight: The smaller the capacitor, the larger the voltage drop across it in a series combination. This is why identical series capacitors share voltage equally.
Formula: Parallel Combination
\[{C_P=C_1+C_2+C_3+\cdots}\]
For n identical capacitors of capacitance C each: CP = nC
Physical Insight: Adding capacitors in parallel is like adding more storage tanks — the total storage capacity simply increases.
Formula: Energy Stored / Work Done in a Capacitor
W = \[\frac {1}{2}\]qV
OR
U = \[\frac {Q^2}{2C}\] = \[\frac {1}{2}\]QV = \[\frac {1}{2}\]CV2
SI unit: Joule (J)
Key Points
Key Points: Electric Potential: A Quantitative Approach
- Electric potential (V) = work done per unit positive test charge, brought from infinity to a point without acceleration: V = \[\frac {W}{q_0}\].
- SI unit: volt (V) = 1 J/C.
- Dimensional formula: [ML2T−3A−1]
- Positive charge flows from higher to lower potential — analogous to liquid flowing downhill or heat flowing from hot to cold.
- Infinity is the standard reference in theoretical electrostatics; Earth is the standard reference in practical circuits and grounding — each valid in its own context.
Key points: Potential and Potential Difference
Key Points: Electric Potential Due to a Point Charge
- Electric potential at a point is the work done per unit positive test charge in bringing it slowly from infinity to that point, against the electric field.
- For a point charge q in air/vacuum:
V(r) = \[\frac{1}{4\pi\varepsilon_0}\frac{q}{r}\] - In a medium of dielectric constant K:
V(r) = \[\frac{1}{4\pi\varepsilon_0K}\frac{q}{r}\] - Positive charge produces positive potential; negative charge produces negative potential.
- Potential due to a point charge is spherically symmetric and depends only on distance r.
- Distance dependence:
F ∝ 1/r2, E ∝ 1/r2, V ∝ 1/r. - The potential at infinity is taken as zero; only potential differences are physically significant.
- The electrostatic field is conservative, so the work done in moving a charge between two points is path independent.
Key Points: Free and Bound Charges
- Free charges → conductors → net internal field = 0.
- Bound charges → dielectrics → polarisation, not conduction.
- Bound charges never leave their parent atom/molecule.
- Polarisation charge is also called induced charge.
- Free charges are the basis of electric current; bound charges are the basis of dielectric behaviour.
Key Points: Dielectrics
- Dielectrics polarise but do not conduct; induced charges oppose (not cancel) the external field.
- Polar dielectrics: pre-existing dipoles align with the field.
- Non-polar dielectrics: dipoles are induced by the field.
- Dielectric constant K = ε/ε0 = E0/E; always K > 1.
- Used in capacitors to reduce field and boost capacitance.
Key Points: Introduction to a Capacitor
- Capacitor stores energy as an electric field; net charge on it is always zero.
- C = q/V depends only on geometry and dielectric, never on q or V.
- Capacitance increases with larger plate area, smaller separation, and higher K.
- Charging stops when capacitor voltage equals source voltage; U = \[\frac {1}{2}\]CV2.
- A nearby (especially grounded) conductor increases capacitance via induction.
- Capacitors are vital for energy storage, filtering, coupling, memory, and wireless tech.
Key Points: Combination of Capacitors
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
Important Questions [8]
- Obtain an Expression for Electric Potential ‘V’ at a Point in an End-on Position I.E. Axial Position of the Electric Dipole.
- Calculate electric potential at a point P which is at a distance of 9 cm from a point charge of 50 μC.
- Define Equipotential Surface.
- What is meant by an equipotential surface?
- Three Capacitors of Capacitance C 1 = 3 μ F , C 2 = 6 μ F , C 3 = 10 μ F , Are Connected to a 10v Battery as Shown in Figure 3 Below :
- Figure 4 Below Shows a Capacitor C, an Inductor L and a Resistor R, Connected in Series to an A.C. Supply of 220 V
- Deduce an Expression for Equivalent Capacitance C When Three Capacitors C1, C2 and C3 Connected in Parallel.
- A wire of resistance ‘R’ is cut into ‘n’ equal parts. These parts are then connected in parallel with each other. The equivalent resistance of the combination is:
Concepts [33]
- Introduction to Electric Potential
- Electric Potential: A Quantitative Approach
- Potential Difference
- Work Done in Moving a Charge in an Electric Field
- Acceleration of a Charged Particle Between Two Points in an Electric Field
- Electric Potential Due to a Point Charge
- Potential due to a Group of Point Charges
- Potential Gradient
- Electric Field as Gradient of Electric Potential: Relation between E and V
- Equipotential Surfaces
- Electric Potential Energy of a System of Charges
- Charged Body Between Parallel Plates
- Potential Due to an Electric Dipole
- Work Done in Rotating an Electric Dipole in an Electric Field
- Electric Potential Energy of an Electric Dipole in an Electrostatic Field
- Electrostatics of Conductors
- Free and Bound Charges
- Dielectrics
- Electric Polarisation of Dielectrics
- Capacitance of a Conductor
- Capacitance of an Isolated Spherical Conductor
- Potential Energy of a Charged Conductor
- Redistribution of Charges: Common Potential
- Introduction to a Capacitor
- The Parallel Plate Capacitor
- Expression for Capacitance of a Parallel-Plate Capacitor
- Dependence of the Capacitance of a Capacitor
- Capacitance of a Parallel-Plate Capacitor with Dielectric Slab between Plates
- Combination of Capacitors
- Energy Stored in a Charged Capacitor
- Force between the Plates of a Charged Parallel-Plate Capacitor
- Effect of Dielectric Insertion on a Capacitor: with and Without a Battery
- Variation of Electric Field and Potential Due to a Charged Sphere
