The idea of electric potential is essential to understand how charges interact in an electric field. The electric potential caused by a point charge is among the most straightforward and vital scenarios to investigate.
What is Electric Potential?
The work required to move a unit positive charge from infinity to a point in an electric field without acceleration is known as the electric potential at that location.
To put it simply, picture a little positive test charge that we gradually approach another charge (for example, a positive or negative one). The electric potential at that location can be incidental from the effort or “work” we put into transferring the test charge.
The SI unit of electric potential is volt (V), and it is a scalar quantity (meaning it has only magnitude, no direction).
Point Charge: What Does That Mean?
An idealistic representation of a particle with a specific quantity of charge but no physical size similar to a charged dot is called a point charge. Since many real objects, such as protons or electrons, may be roughly represented as point charges.
Formula for Electric Potential Due to a Point Charge
If we have a point charge Q placed at some location, then the electric potential V at a distance r from the charge is given by the formula:
V = 1 / 4πε0 ⋅ Q / r
Where:
V is the electric potential,
Q is the point charge,
r is the distance from the charge to the point where we are measuring the potential,
ε0 is the permittivity of free space, a constant with value 8.85×10−12 C2/N,
The constant 1 / 4πε0 ≈ 9×109 N \C2 we can also write:
V = 9 × 109 ⋅ Q / r
Understanding the Formula
Assume that we are positively charged. Because like charges repel one another, we have to put in more effort as we get a little positive test charge closer to it. For this reason, as we approach a positive charge, the potential rises.
If Q is positive, the potential is positive.
If Q is negative, the potential is negative.
This tells us whether the electric field would help or resist the motion of a positive test charge.
Graph of Potential vs. Distance
With increasing distance, a point charge’s electric potential reduce. An illustration of V vs. r might resemble a curve that decreases as r rises. This is due to the fact that the charge has less of an impact on a point in space the farther we are from it.
Important Points to Remember
Scalar Quantity: The electric potential is scalar, in contrast to the vector electric field. Therefore, we may just add the numbers without caring about direction when adding potentials from various charges.
Reference Point: The potential at infinity is typically assumed to be zero. This simplifies computations.
Positive vs. Negative Potential:
A positive potential means work has to be done against the field.
A negative potential means the field is doing work for
Superposition Principle: If multiple point charges are present, the total potential at a point is just the algebraic sum of potentials due to individual charges.
Vtotal = V1 + V2 + V3+…
Example Problem
Q: What is the electric potential at a distance of 1 m from a point charge of 2 μC?
A:
Given: Q = 2 × 10 − 6 C
r = 1 m
V = 1 / 4πε0 ⋅ Q / r = 9 × 109 ⋅ 2 × 10−61 = 18,000 V
So, the electric potential is 18,000 volts.
Summary
A point charge’s electric potential aids in our comprehension of the energy environment surrounding charged particles. It indicates the amount of energy required to position another charge close to that charge at a certain location in space. It is a fundamental idea that will support our studies of electric potential energy, capacitors.
It describes the effort required to move a unit positive charge without acceleration from infinity to a point in the electric field produced by a point charge. It displays the amount of potential energy that a charge would possess at that particular moment.
The electric 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.
The SI unit of electric potential is the volt (V).
1 volt = 1 joule per coulomb (1 V = 1 J/C)
Electric potential is a scalar quantity, meaning it has magnitude only and no direction.
By convention, the electric potential at infinity is taken as zero. This helps simplify calculations and comparisons.
The electric potential decreases with increasing distance from the point charge, following an inverse relationship: V ∝ 1 / r.
Electric potential tells us how much energy a charge would have at a point.
Electric field tells us the force a unit charge would experience.
Also, electric potential is scalar, while electric field is a vector.