The area of physics that studies electric charges at rest is called electrostatics. Electrostatic potential is a key idea in electrostatics. It aids in our comprehension of the amount of effort needed to move a charge across an electric field.
Electrostatic potential (V) at a point = work done by an external force in bringing a unit positive charge from infinity to that point.
Potential at appoint is the potential difference between the potential at the point and the potential at infinity.
Electric potential difference between any points in an electric field is the amount of work done in moving a unit positive test charge from any path against the electrostatic forces.
What is Electrostatic Potential?
The amount of work required to move a unit positive charge from infinity to a point against the electric field without any acceleration is known as the electrostatic potential at that location.
It is a scalar quantity (has only magnitude, no direction).
The SI unit of electrostatic potential is volt (V).
One volt is defined as 1 joule of work done in bringing 1 coulomb of charge.
Formula: V = W / q
Where:
V = Electrostatic potential
W = Work done
q = Charge
If we are bringing a unit positive test charge (q = 1 C), then:
V = W
Electrostatic Potential Due to a Point Charge
Suppose we have a point charge Q, and we want to find the potential at a point at a distance r from it. The formula is:
V = 1 / 4πε0 ⋅ Q / r
Where:
ε0 = Permittivity of free space ( ≈ 8.854 × 10−12 C2 / N ⋅ m2)
1 / 4πε0 ≈ 9 × 109 Nm2 / C2
So, the potential due to a positive charge is positive, and due to a negative charge is negative.
Electrostatic Potential Difference
This is the difference in potential between two points in an electric field. VA – VB = W / q
This tells us how much work is required to move a charge from point B to point A. A higher potential means more electric potential energy.
Equipotential Surfaces
These are imaginary surfaces where the electric potential is the same at every point.
No work is done in moving a charge along an equipotential surface.
The electric field is always perpendicular to the equipotential surface.
For a point charge, equipotential surfaces are spherical shells centered at the charge
Relation Between Electric Field and Potential
Potential and electric field are connected. The electric potential’s negative gradient is known as the electric field.
E = −dV / dr
This means that the electric field points in the direction of decreasing potential.
If the potential changes rapidly with distance, the electric field is strong.
Electrostatic Potential Energy
Because of their placements, two charges that are positioned close to one another interact and cause energy to be stored in the system. Electrostatic potential energy is the term for this.
For two point charges q1 and q2 separated by distance r:
U = 1 / 4πε0 ⋅ q1q2 / r
The potential energy is positive (they repel) if both charges have the same sign.
• Potential energy is negative (they attract) if their signs are opposing.
Key Points to Remember
At infinity, potential is regarded as zero.
• From high potential to low potential, a positive charge shifts.
• Naturally, a negative charge flows from low potential to high potential.
• In electrostatics, work is path-independent and only reliant on initial and terminal positions.
Applications
Designing electrical circuits, capacitors, medical devices (such as defibrillators), and computer parts (such as memory chips) all require an understanding of electrostatic potential.
We can see how charges interact in an electric field with the aid of electrostatic potential. It is a fundamental idea for additional research in electromagnetic, electronics, and electricity.
The work required to move a unit positive charge from infinity to a specific location in an electric field without acceleration is known as the electrostatic potential at that location. The potential energy per unit charge is shown.
SI Unit: Volt (V)
1 Volt = 1 Joule / Coulomb
Dimensional Formula: [ML2T−3A−1]
The electric field is the negative rate of change of potential with respect to distance: E = −dV / dr
This means the electric field points in the direction where the potential decreases fastest.
The electrostatic potential V at a distance r from a point charge Q is given by:
V = 1 / 4πε0 ⋅ Q / r
Where ε0 is the permittivity of free space.
Equipotential surfaces are imaginary surfaces where every point has the same electrostatic potential.
No work is done when moving a charge along an equipotential surface.
The electric field is always perpendicular to these surfaces.