- 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 [11]
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 potential difference between those two points.
Definition: Electric Dipole
An electric dipole is a pair of equal and opposite point charges, placed at a small distance. Its moment, known as electric dipole moment.
OR
A system of two equal and opposite charges separated by a small distance, is called an electric dipole.
Definition: Electric Dipole Moment
The product of the magnitude of one charge and the separation vector directed from negative to positive charge, is called the electric dipole moment.
\[\vec p\] = q × (2\[\vec a\])
Definition: Electric Potential at a Point
The work done by an external agent in carrying a unit positive test charge from infinity to a point in the electric field is called the electric potential at that point.
OR
The work done in bringing a unit positive charge (without acceleration) from infinity to a given point in an electric field, is called electrostatic potential at that point.
Definition: Potential Gradient
The rate of change of potential with distance in the electric field is called the 'potential gradient'.
Definition: Electric Potential Energy
The electric potential energy of a system of charges is the work that has been done in bringing those charges from infinity to near each other to form the system.
OR
The total work done by an external agency in assembling the charges from infinity to their specified positions (without acceleration), is called the electrostatic potential energy of the system.
Definition: Equipotential Surface
Any surface over which the electric potential is same everywhere is called an equipotential surface.
OR
A surface on which the electric potential has the same value at every point, is called an equipotential surface.
Definition: Electron-volt
1 electron-volt is the work done in taking one electron from one point to the other, when the potential difference between these points is 1 volt.
OR
1 electron-volt is the (kinetic) energy which an electron acquires when accelerated through a potential difference of 1 volt.
Formulae [11]
Formula: Electric Potential at a Point
V = \[\frac {W}{Q}\]
or
W = QV
Formula: Electric Potential Due to a Point Charge
V = \[\frac{1}{4\pi\varepsilon_0}\frac{q}{r}\] volt
Formula: Work Done in Rotating an Electric Dipole
W = pE (cos θ1 – cos θ2)
Formula: Potential Due to a System of Charges
Potential due to a continuous charge distribution:
\[V=\frac{1}{4\pi\varepsilon_0}\int\frac{\rho dV}{r}\]
Potential outside a uniformly charged spherical shell:
\[V=\frac{1}{4\pi\varepsilon_0}\frac{q}{r}\quad(r\geq R)\]
Potential inside a uniformly charged spherical shell:
\[V=\frac{1}{4\pi\varepsilon_0}\frac{q}{R}\quad(r<R)\]
Formula: Relation between Electric Field and Potential
E = -\[\frac {dV}{dl}\]
Formula: Dipole Potential on Axial Line
V = \[\frac{1}{4\pi\varepsilon_0}\frac{P}{r^2-l^2}\]
Far-field, r ≫ 2l: V = \[\frac{1}{4\pi\varepsilon_{0}}\frac{p}{r^{2}}\] volt.
Formula: Potential Difference between Two Points
\[V_A-V_B=\frac{W}{q_0}\]
OR
\[V_P-V_R=\frac{U_P-U_R}{q}\]
Formula: Electron-volt
1 electron-volt = 1.6 × 10-1 joule.
Formula: Electric Potential Energy of Two Point Charges
U = \[\frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}q_{2}}{r}joule\]
Formula: Potential at any Point
V = \[\frac{1}{4\pi\varepsilon_{0}}\frac{p\cos\theta}{r^{2}}\] volt.
Formula: Electric Potential
V = \[\frac {W}{q_0}\]
- Dimensions: [V] = [ML2T−3A−1]
- SI unit is volt (V), where 1 V =1 J C−1
OR
\[V=\frac{W_{\infty\to P}}{q}\]
Unit: 1 volt=1 joule per coulomb (J/C)
Key Points
Key points: Potential and Potential Difference
Key Points: Properties of Equipotential Surfaces
- Zero Work: No work is done in moving a charge along an equipotential surface because the potential difference is zero.
- Relation with Electric Field: The electric field is always perpendicular to an equipotential surface; there is no electric field component along the surface.
- Spacing and Field Strength: Equipotential surfaces are closer where the electric field is strong and farther apart where the field is weak.
- Non-intersection: Equipotential surfaces never intersect, since that would imply two directions of the electric field at one point, which is impossible.
Key Points: Electric Potential Energy of an Electric Dipole at Electrostatic Field
- The potential energy of an electric dipole in a uniform electric field is
U = − p ⋅ E = − pE cos θ - When the dipole is parallel to the field (θ = 0∘),
U = − pE
This is the minimum potential energy (stable equilibrium). - When the dipole is perpendicular to the field (θ = 90∘),
U = 0 - When the dipole is anti-parallel to the field (θ = 180∘),
U = +pE
This corresponds to an unstable equilibrium. - Work done in rotating the dipole through an angle θ\thetaθ is W = pE(1 − cosθ) and this work equals the increase in potential energy.
