How to Calculate Electric Potential from a Point Charge: Step-by-Step Guide
What is Electric Potential and How it Works?
The electric potential, or voltage, is the distinction in potential energy per unit charge between two areas in an electric field. At the point when we discussed the electric field, we selected a location and afterward asked what the electric power/force would do to an imaginary positively charged particle if we placed one there.
To measure the electrical potential at a selected spot, we ask how much the electrical possible energy of an imaginary positively charged particle would change if we moved it there. Much the same as when we discussed the electric field, we don't really need to put a positively charged particle at our selected spot to know how much electrical potential energy it would have.
Reason for Change
We realize that the measure of charge we are pushing or pulling (and whether it is positive or negative) has any kind of effect on the electrical potential energy if we move the molecule to a selected spot. That is the reason physicists utilize a single positive charge as our imaginary charge to try out the electrical potential at some random point. That way we just need to stress over the measure of charge on the plate, or whatever charged item we're considering.
Impact on Electric Potential
Suppose we have a negatively charged plate. We realize that a positively charged molecule will be pulled towards it. That implies we realize that if we select a spot close to the plate to put our imaginary positively charged particle, it would have a smidgen of electrical potential energy, and if we select a spot further away, our imaginary positively charged molecule would have increasingly more electrical energy. So we can say that close to the negative plate the electrical potential is low, and further from the negative plate, the electrical potential is high.
Electric potential is, for the most part, a trait of the electric field. It is free of the reality whether a charge ought to be set in the electric field or not. Electric potential is a scalar quantity. At point charge +q there is consistently a similar potential at all points with a distance r.
Electric Potential Due to Point Charge
The electric potential at a point in an electric field is characterized as the measure of work done in moving a unit positive charge from infinity to that point along any path when the electrostatic powers/forces are applied. Assume that a positive charge is set at a point. The charge set by then will apply a power/force because of the presence of an electric field. The electric potential anytime at a distance r from the positive charge +q is appeared as:
It is given by the formula as stated,
V=1*q/4πϵ0*r
Where,
The position vector of the positive charge = r
The source charge = q
As the unit of electric potential is volt,
1 Volt (V) = 1 joule coulomb-1(JC-1)
At the point when work is done in moving a charge of 1 coulomb from infinity to a specific point because of an electric field against the electrostatic power/force, at that point it is supposed to be 1 volt of the electrostatic potential at a point.
Electric Potential Because of Multiple Charges
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When there is a
q1, q2, q3,… .qn as a group of point charges
And is kept at
Distance r1, r2, r3,… … rn,
We can get the electrostatic potential at a specific point. We can locate the electrostatic potential at any point because of every individual charge by considering different other charges as absent. We at that point include all the charges mathematically.
Henceforth, the electric potential at a point because of a group of point charges is the mathematical total of all the potentials because of individual charges.
It is stated as,
V = \[\frac{1}{4π∊₀}\] \[\sum_{i=1}^{n}\] \[\frac{q_{i}}{r_{i}}\]
FAQs on Electric Potential Due to a Point Charge Explained
1. What is meant by electric potential due to a point charge?
The electric potential due to a point charge at any point in space is defined as the amount of work done by an external force in bringing a unit positive test charge from infinity to that point, without any acceleration. It is a scalar quantity that describes the potential energy per unit charge at a specific location. Its SI unit is the Volt (V).
2. What is the formula for calculating the electric potential of a point charge?
The formula to calculate the electric potential (V) at a distance (r) from a single point charge (q) is given by:
V = k * (q/r)
Where:
- V is the electric potential.
- k is Coulomb's constant, approximately 9 × 10⁹ N·m²/C².
- q is the magnitude of the point charge.
- r is the distance from the point charge to the point where the potential is being measured.
3. How is the formula for electric potential due to a point charge derived as per the CBSE 2025-26 syllabus?
The derivation involves calculating the work done to move a unit charge from infinity to a point 'P' at distance 'r' from a source charge 'q'.
- Step 1: By definition, electric potential V is the negative of the work done by the electric field, V = -∫(∞ to r) E ⋅ dr.
- Step 2: The electric field (E) due to a point charge 'q' at a distance 'x' is E = kq/x².
- Step 3: Substitute E into the integral: V = -∫(∞ to r) (kq/x²) dx.
- Step 4: Since k and q are constants, they are taken out of the integral: V = -kq ∫(∞ to r) (1/x²) dx.
- Step 5: The integral of 1/x² is -1/x. Evaluating this from ∞ to r gives: V = -kq [-1/x] from ∞ to r.
- Step 6: This results in V = -kq [(-1/r) - (-1/∞)]. Since 1/∞ is 0, we get V = -kq[-1/r].
- Step 7: Simplifying this gives the final formula: V = kq/r.
4. What is the key difference between electric potential and electric potential energy?
While related, electric potential and electric potential energy are distinct concepts:
- Electric Potential (V): It is a characteristic of a point in space created by a source charge. It represents the work done per unit charge (Joules/Coulomb or Volts). It tells you how much potential energy a charge *would have* if placed at that point.
- Electric Potential Energy (U): It is a property of a system of two or more charges. It is the total work done to assemble the system of charges from an infinite separation. Its unit is Joules (J). The relationship is U = qV.
5. Why is the electric potential at an infinite distance from a point charge taken as zero?
The concept of potential is relative and requires a reference point. We choose infinity as the zero-potential reference point for convenience and physical sense. At an infinite distance, the electric force and electric field due to the point charge diminish to zero. Therefore, no work is required to move a test charge in that region, making it the most logical point to define as having zero potential.
6. How does the sign of a point charge (positive or negative) influence the electric potential it creates?
The sign of the point charge directly determines the sign of the electric potential:
- A positive point charge (+q) creates a positive electric potential in the space around it. The potential is highest near the charge and decreases as the distance increases.
- A negative point charge (-q) creates a negative electric potential. The potential is most negative (lowest value) near the charge and increases towards zero as the distance increases.
7. What does the constant 'k' in the electric potential formula, V = kq/r, represent?
The constant 'k' is known as Coulomb's constant or the electrostatic force constant. It is a proportionality constant that relates electric force and potential to charge and distance in a vacuum. Its value is approximately 9 × 10⁹ N·m²/C². It is also expressed as k = 1 / (4πε₀), where ε₀ is the permittivity of free space.
