Electric Potential and Potential Difference Explained
Electric potential is the work done per unit charge to move a charge from infinity to a point in an electric field. Potential difference is the difference
TL;DR: Electric potential is the work done per unit charge to move a charge from infinity to a point in an electric field. Potential difference is the differ…
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Electric Potential and Potential Difference: Electric potential is the work done per unit charge to move a charge from infinity to a point in an electric field. Potential difference is the difference
Electric Potential and Potential Difference Explained Simply
Electric potential is the work done per unit charge to move a charge from infinity to a point in an electric field. Potential difference is the difference This is a key Physics concept for Class 12.
What is Electric Potential?
Electric potential at a point is defined as the work done per unit positive charge in bringing a test charge from infinity to that point in an electric field. It is a scalar quantity measured in volts (V). One volt means 1 joule of work is done to move 1 coulomb of charge. Electric potential is independent of the path taken, depending only on the initial and final positions.
Electric Potential Difference
Potential difference between two points A and B is defined as the work done per unit charge in moving a positive charge from point B to point A. If V_A and V_B are potentials at A and B, then potential difference V_AB = V_A - V_B, measured in volts. In a circuit, this is the voltage across a component.
Relationship with Electric Field
Electric field and electric potential are related by the equation E = -dV/dx, where E is electric field strength and dV/dx is the rate of change of potential with distance. In a uniform electric field, V = -Ex + constant. The electric field always points from higher potential to lower potential. The stronger the field, the steeper the potential gradient.
Potential due to Point Charge
For a point charge Q at distance r, the electric potential is V = kQ/r, where k = 9 x 10^9 N m^2 C^-2. This potential is positive for positive charges and negative for negative charges. As distance increases, potential decreases inversely with distance. The potential due to multiple charges is the algebraic sum of potentials due to individual charges.
Equipotential Surfaces
An equipotential surface is an imaginary surface where all points have the same electric potential. No work is required to move a charge along an equipotential surface. Equipotential surfaces are always perpendicular to electric field lines. Around a point charge, equipotential surfaces are concentric spheres centered on the charge.
Application in Electric Circuits
In circuits, potential difference drives current through resistors and other components. The total potential difference supplied by a battery equals the sum of potential differences across all circuit elements. This principle is the basis of Kirchhoff's voltage law, which states that the sum of potential differences around a closed loop is zero.
Worked Examples
Example 1. Calculate the electric potential at a distance of 0.1 m from a point charge of 2 microcoulombs. (k = 9 x 10^9 N m^2 C^-2)
Solution: Given: Q = 2 μC = 2 x 10^-6 C, r = 0.1 m, k = 9 x 10^9 N m^2 C^-2
Using V = kQ/r
V = (9 x 10^9 x 2 x 10^-6) / 0.1
V = (18 x 10^3) / 0.1
V = 180,000 V = 1.8 x 10^5 V
Example 2. The potential difference between two points in an electric field is 100 V. How much work is done in moving a charge of 5 coulombs from lower to higher potential?
Solution: Given: V_AB = 100 V, Q = 5 C
Work done W = Q x V_AB
W = 5 x 100
W = 500 J
Since we move from lower to higher potential (against field), external work of 500 J must be done.
Example 3. Two point charges +4 μC and -4 μC are placed 20 cm apart. Find the potential at the midpoint between them.
Solution: Given: Q1 = +4 μC, Q2 = -4 μC, distance between charges = 20 cm, so distance from each to midpoint = 10 cm = 0.1 m
Potential at midpoint = V1 + V2 = kQ1/r + kQ2/r
V = (9 x 10^9 x 4 x 10^-6)/0.1 + (9 x 10^9 x (-4) x 10^-6)/0.1
V = 360,000 - 360,000 = 0 V
The potential at the midpoint is zero (dipole configuration).
Where You See This in Real Life
- When you get an electric shock, it is due to potential difference between your body and the ground causing current to flow through you.
- In household circuits in India, the standard potential difference is 230 V AC, which determines how much power electrical appliances can use.
- Lightning occurs when potential difference between clouds and Earth becomes so large (millions of volts) that air ionizes and breaks down.
- Car batteries in India provide a potential difference of 12 V DC to start the engine and power electrical systems.
Common Mistakes Students Make
- Confusing electric potential with electric field. Potential is energy per charge (scalar), while field is force per charge (vector).
- Not considering the sign of charge when calculating potential. Positive charges create positive potential, negative charges create negative potential.
- Forgetting that potential difference is a relative quantity between two points, not an absolute value at a single point.
- Using potential instead of potential difference in circuit analysis, which leads to incorrect calculations of current and power.
Frequently Asked Questions
What is the SI unit of electric potential?
The SI unit is volt (V), named after Alessandro Volta. One volt equals one joule per coulomb (1 V = 1 J/C).
Can electric potential be negative?
Yes, electric potential can be negative. It depends on the sign of the source charge and the reference point chosen (usually infinity is taken as zero potential).
Why is equipotential surface perpendicular to electric field lines?
Because if a surface were not perpendicular to field lines, there would be a component of electric field along the surface, meaning work would be done moving charge on that surface. But by definition, no work is done on equipotential surfaces, so they must be perpendicular to field lines.