How Is Electric Potential Calculated?
Electric potential is a core concept in electrostatics, essential for understanding electric fields and energy in Physics. It enables the calculation of work done by electric forces, energy transfer, and helps solve a range of problems for JEE Main and Advanced.
Definition of Electric Potential
Electric potential at a point is defined as the work done by an external agent in bringing a unit positive charge from infinity to that point against the electrostatic force. It is a scalar quantity and measured in volts (V), where $1~\text{V} = 1~\text{J}~\text{C}^{-1}$.
Electrostatic Potential: Mathematical Expression
The electric potential, $V$, at a point in an electric field is given by the equation:
$V = \dfrac{W}{q}$
Here, $W$ is the work done in joules and $q$ is the test charge in coulombs.
Units and Dimensions of Electric Potential
The SI unit of electric potential is volt (V), which is equivalent to joule per coulomb. The dimensional formula is $[ML^2T^{-3}A^{-1}]$.
| Physical Quantity | Unit |
|---|---|
| Electric potential | Volt (V) |
| Potential difference | Volt (V) |
| Electric potential energy | Joule (J) |
Electric Potential Due to a Point Charge
The electric potential at a distance $r$ from a point charge $Q$ in vacuum is given by:
$V = \dfrac{1}{4\pi \varepsilon_0} \dfrac{Q}{r}$
Here, $\varepsilon_0$ is the permittivity of free space. The value of $\dfrac{1}{4\pi\varepsilon_0}$ is approximately $9 \times 10^9~\text{N m}^2\text{C}^{-2}$.
Electric Field Lines Explanation can be used to visualize the relationship between electric potential and field.
Electric Potential Due to Multiple Point Charges
For a system of $n$ point charges $Q_1, Q_2, ..., Q_n$ at distances $r_1, r_2, ..., r_n$ from point $P$, the net potential is the algebraic sum:
$V = \dfrac{1}{4\pi \varepsilon_0} \left( \dfrac{Q_1}{r_1} + \dfrac{Q_2}{r_2} + ... + \dfrac{Q_n}{r_n} \right )$
Electric potential being a scalar quantity can be added directly, unlike electric field, which follows vector addition. Related concepts are available in the Electrostatics Overview.
Electric Potential Difference
The electric potential difference (voltage) between two points $A$ and $B$ is defined as the work done per unit charge to move a test charge from $A$ to $B$. It is given by:
$V_{BA} = V_B - V_A = \dfrac{W_{AB}}{q}$
Potential difference drives the motion of charges in circuits and fields. It is measured in volts. More information on field concepts is provided in Electric Field Due to Infinite Plane.
Electric Potential Energy: Concept and Formula
Electric potential energy is the energy stored due to the position of a charge in an electric field. When two charges $q_1$ and $q_2$ are separated by a distance $d$, their potential energy is:
$U = \dfrac{1}{4\pi \varepsilon_0} \dfrac{q_1 q_2}{d}$
For a charge $q$ at a point where the electric potential is $V$, the potential energy is $U = qV$. The units are joule (J). For energy in dipole systems, refer to Potential Energy of Electric Dipole.
Relation between Electric Potential and Electric Field
The electric field $\vec{E}$ at a point is related to the rate of change of electric potential $V$ with distance. In one dimension,
$E = -\dfrac{dV}{dr}$
The negative sign indicates that the electric field points in the direction of decreasing potential. A full revision of electrostatics is available at Electrostatics Revision Notes.
Electric Potential in Conductors and Insulators
Inside a conductor under electrostatic equilibrium, the electric potential remains constant throughout. No electric field exists inside the conductor in this state. In insulators, charges do not move freely, and potential changes may occur across the material.
Applications and Problem Solving
Various problems in JEE ask to calculate potential due to distributed charges and systems like spheres, shells, or parallel plates. Mastery of the electric potential equation and superposition is essential for these problems. Further discussions can be explored in Understanding Capacitance.
Electric Potential vs Electric Potential Energy
Electric potential is the work done per unit charge, while electric potential energy is the total energy possessed by a charge due to its position. The key difference lies in dependency: potential is independent of test charge, whereas potential energy depends on the amount of charge.
| Electric Potential | Electric Potential Energy |
|---|---|
| Work done per unit charge | Total energy of charge configuration |
| Unit: volt (V) | Unit: joule (J) |
| Scalar quantity | Scalar quantity |
Key Formulas in Electric Potential
Important equations are frequently used for solving JEE Main and Advanced problems:
- Potential at distance $r$: $V = \dfrac{1}{4\pi \varepsilon_0} \dfrac{Q}{r}$
- Work, charge, potential: $W = qV$
- Potential difference: $V = \dfrac{W}{q}$
- Potential energy (two charges): $U = \dfrac{1}{4\pi \varepsilon_0} \dfrac{q_1 q_2}{d}$
- Relation to field: $E = -\dfrac{dV}{dr}$
Summary and Further Resources
Understanding electric potential, its relation to electric field, and energy is fundamental in solving electrostatics problems. This includes both point and continuous charge distributions. For further practice and summary, refer to the detailed Electrostatics Revision Notes.
FAQs on Understanding Electric Potential in Physics
1. What is electric potential?
Electric potential is the amount of work needed to move a unit positive charge from infinity to a point in an electric field. In simple terms, it tells us how much energy a charge will have at a specific point.
Key points:
- It is measured in volts (V)
- It is a scalar quantity
- Given by the formula V = W/q, where W is work done and q is charge
- Higher electric potential means more potential energy for a charge at that point
- Relevant for understanding electric field, potential difference, and electrostatics
2. What is the difference between electric potential and electric potential difference?
Electric potential is the energy per unit charge at a specific point, while electric potential difference (voltage) is the change in potential between two points.
Important distinctions:
- Potential at a point (V) refers to energy per coulomb at that location
- Potential difference (ΔV) indicates how much energy moves from point A to B
- Only potential difference is physically measurable, not absolute potential
- Calculated as ΔV = VB – VA
- Strongly linked to the movement of charges and circuit concepts
3. How do you calculate electric potential due to a point charge?
The electric potential (V) at a distance r from a point charge Q is given by:
V = (1/4πε₀) × (Q/r)
Where:
- Q = charge (in coulombs)
- r = distance from the charge (in metres)
- ε₀ = permittivity of free space
This formula helps calculate potential around point charges and is key in electrostatics problems.
4. What are the units of electric potential and how are they defined?
The SI unit of electric potential is the volt (V).
Definitions and details:
- 1 volt = 1 joule per coulomb (1 V = 1 J/C)
- Shows the work needed to bring 1 coulomb of charge by 1 joule of energy
- Expressed mathematically as V = W/q
- Used widely in CBSE, NEET, and JEE exam questions
5. What is the physical significance of electric potential?
The physical significance of electric potential is that it represents the potential energy per unit charge at any point in an electric field.
Main points:
- Indicates work done in moving a charge
- Helps compare energy status at different points
- Determines how charges move in electric fields
- A high potential means charge has more potential energy at that point
- Useful in analysing electrostatic phenomena and circuits
6. How is electric potential related to electric field?
The electric field (E) is the rate of change of electric potential (V) with distance.
Relationship:
- E = -dV/dr (in calculus form for one dimension)
- The field points in the direction of decreasing potential
- A steeper potential gradient means a stronger electric field
- Used in both numerical and theoretical exam questions
7. Can electric potential be negative or zero?
Yes, electric potential can be positive, negative, or zero based on the reference point and type of charges.
- For a positive charge, potential around it is positive
- For a negative charge, potential around it is negative
- At some points (like infinity or specific midpoints), potential can be zero
- Sign of potential helps predict how charges will move
8. Why is the potential at infinity taken as zero?
The potential at infinity is taken as zero by convention to provide a common reference for measuring potential.
Reasons:
- Simplifies calculations and avoids negative values for energy
- Makes comparison between different points possible
- Standard approach used in CBSE and NCERT syllabus for consistency
- Helps define absolute and relative potentials in physics problems
9. What factors affect electric potential at a point?
The electric potential at any point depends on several important factors:
- Amount of charge (Q)
- Distance from the charge (r)
- Medium between the plates or charges (permittivity, ε)
- Geometry of the charge configuration
Understanding these helps master electrostatics questions in exams.
10. What are equipotential surfaces?
An equipotential surface is a surface with the same electric potential at every point.
Main features:
- No work is done moving a charge on an equipotential surface
- Always perpendicular to the electric field lines
- Common examples: surfaces around a point charge or parallel to plates in a capacitor
- Useful in practical problem-solving and theory-based exam questions
