- 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 [10]
Definition: Potential Difference
The difference in electrical potentials between two points is known as potential difference or voltage.
The unit of potential difference or potential is joule/coulomb, called a volt (V).
Definition: Electric Potential
Electric potential at a point is the work done in bringing a unit positive test charge from infinity to that point in an electric field.
The SI unit of electric potential is the volt.
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.
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’.
Definition: Potential at a Point
The potential at a point is defined as the amount of work done per unit charge in bringing a positive test charge from infinity to that point.
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.
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: Equipotential Surface
The surface at which electric potential is the same at each point is called an equipotential surface.
Definition: Electric Dipole
An electric dipole is a pair of equal and opposite charges separated by a small distance.
Definition: Dipole Length
If the charges are separated by a distance 2a2a, then 2a2a is called the dipole length.
Formulae [10]
Formula: Potential at a Point Due to a System of Charges
\[V=\frac{1}{4\pi\varepsilon_0}\sum_{i=1}^n\frac{q_i}{r_i}\]
Formula: Potential Due to a Dipole
\[V=\frac{q(2a\cos\theta)}{4\pi\varepsilon_0(r^2-a^2\cos^2\theta)}\]
if r ≫ a:
\[V=\frac{p\cos\theta}{4\pi\varepsilon_0r^2}\]
Formula: Electric Potential at a Point
V = \[\frac {W}{Q}\]
or
W = QV
Formula: Potential Due to a Point Charge
\[V=\frac{Q}{4\pi\varepsilon_0r}\]
Potential due to System of Charges:
\[U=\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r_{12}}\]
Formula: Electric Potential Energy of Two Point Charges
U = \[\frac{1}{4\pi\varepsilon_0}\cdot\frac{q_1q_2}{r_{12}}\]
Formula: In a medium of dielectric constant K K
\[V(r)=\frac{1}{4\pi\varepsilon_0K}\frac{q}{r}\]
- 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.
Formula: Electric Potential due to a Point Charge
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 = \[\frac {1}{4πε_0}\] ⋅ \[\frac {q}{r}\]
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 Due to an Electric Dipole
\[V=\frac{1}{4\pi\varepsilon_{0}}\cdot\frac{p\cos\theta}{r^{2}}=\frac{1}{4\pi\varepsilon_{0}}\cdot\frac{\vec{p}\cdot\vec{r}}{r^{3}}(r>>a)\]
Formula: Electric Dipole Moment
The electric dipole moment is:
\[\vec{p}=q(2a)\hat{p}\]
Its direction is from the negative charge to the positive charge.
Key Points
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.
Important Questions [4]
Concepts [12]
- Electric Potential
- Potential and Potential Difference
- Electron-volt or eV
- 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
- Electric Potential Energy of a System of Charges
- Equipotential Surfaces
- 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
