An electrostatic potential is also known as an electric field potential, an electric potential, or a potential drop. Electrostatic potential at a point is the work done per unit positive test charge in bringing it from infinity to that point in the electric field of stationary charges without any change in kinetic energy. It represents the potential energy available for a unit charge at that location and determines how charges will move within the field.
Electric potential refers to the amount of electric “push” or “pull” present at a particular point in space. It indicates how a charged particle would behave if placed at that point. In simple terms, it tells us how strongly a charge is encouraged to move or remain at rest. Electric potential helps us understand the interaction of charges and their behavior within an electric field.
Formula For Electrostatic Potential
The formula for electrostatic potential, often denoted as V, is given by
V = \frac{kQ}{r} = \frac{1}{4\pi\varepsilon_0}\,\frac{Q}{r}
where,
- V represents the electrostatic potential at a point.
- k is Coulomb's constant (a proportionality constant),
- Q is the magnitude of the point charge creating the electric field, and
- r is the distance from the point charge to the point of electric po
Electric Potential at a Point
Electric potential at a point is defined as the work done per unit charge in bringing a positive test charge from infinity to that point in an electric field. Mathematically, the electric potential V is defined as follows.
V = \frac{U}{q}
The SI unit of electric potential is the volt (V), which is equal to joule per coulomb (J/C). Electric potential is a scalar quantity, and its sign indicates whether the point is at a higher (positive) or lower (negative) potential relative to a reference point.
Potential Due to Point Charge
A point charge produces an electric field around it, and every point in this field has an associated electric potential called electrostatic potential. The electric potential due to a point charge Q at a distance r is given by
Unit of Electric Potential
The unit of electric potential is volt (V). It represents the potential difference between two points in an electric field.
\text{Volt (V)} = \frac{\text{Joule (J)}}{\text{Coulomb (C)}}
Dimension of Electric Potential
The dimension formula of electric potential is ML2T-3A-1
Factors Influencing Electrostatic Potential
- Magnitude of charge: Electric potential is directly proportional to the magnitude of the charge producing the field.
- Distance from the charge: Electric potential decreases with an increase in distance from the charge (varies as 1/r).
- Presence of other charges: Nearby charges modify the net potential by superposition.
- External fields: External electric fields can alter the charge arrangement, changing the electrostatic potential.
Electric Potential Energy
Electric potential energy is the stored energy that results from the position or configuration of charged particles within an electric field. It arises due to the interaction between these charged particles and the electric field in which they are situated. The electric potential energy of a charged particle depends on its position relative to other charged particles and the strength of the electric field.
Electrostatic potential energy formula:
U_E = k \frac{q_1q_2}{r}
where,
- UE = the electric potential energy
- q1 and q2 = electric charges
- r = Distance between q1 & q2
Electric Potential vs. Electric Potential Energy
Basis | Electric Potential | Electric Potential Energy |
|---|---|---|
Dependence on Charge | It depends only on the source charge(s) creating the electric field and the distance from the point of interest. | It depends not only on the charges creating the electric field but also on the test charge or system of charges experiencing the field. |
Nature | It is a scalar quantity, representing the intensity of the electric field at a given point. | It is a scalar quantity, representing the stored energy in a system of charges due to their configuration in an electric field. |
Representation | It represents the electric field intensity at a particular point. | It represents the stored energy in a system of charges. |
Relation | It is related to electric potential energy per unit charge, as V = U/q, where V is electric potential, U is electric potential energy, and q is charge. | It contributes to the electric potential, as the electric potential at a point is directly related to the electric potential energy per unit charge at that point. |
Calculation | It's calculated by dividing the electric potential energy by the amount of charge present. | It's calculated by summing up the work done in bringing individual charges together from infinity to their respective positions. |
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Solved Problems
Problem 1: Calculate the electric potential at a point located 4m away from a point charge of 5— μC.
Solution: Given:
Point charge = 5μC = 5 × 10 -6 C
Distance from the point charge to the point where the potential is to be calculator: r= 4m
Vacuum permittivity ε0 = 8.854×10 −12 C2 /N⋅m2
Electric potential formula: V = KQ/r1. Convert the charge to coulombs if necessary: Q = 5 × 10 -6 C
2. Use the formula for electric potential: V = K.q/r
3. Substitute the given values: V = (8.99 × 10 9) × (5 × 10 -6)/4m
4. Calculate the result: V = (8.99 × 10 9) × (5 × 10 -6)/4
⇒ V = 11.2375 × 10 3 V
5. Convert the result to kilovolts (kV): V = 11.2375 kV
The electric potential at a point located 4m away from a point charge of 5μC is 11.2375kV
Problem 2: Determine the electric potential at 0.001 m for a charge of 2 pC.
Solution: By the formula,
V = kq/r
we can conclude that, by :K= 9 × 10 9
1p = 1 × 10 -12 (picometre)
hence,
V = 9 × 109(2 × 10 -12)/(0.001) = 18 volts
Problem 3: If a second charge (-2 pC) was the same distance from the point of interest as the first charge, find the total electric potential at that point.
Solution: The total potential is the algebraic sum of the potential caused by each charge:
V = Σkq/r
Since the distances are the same for each charge, but the sign is opposite, the total potential is zero in this case.
Problem 4: Two charges are located on the corners of a rectangle with a height of 0.05 m and a width of 0.15 m. The first charge (q1= -5×10-6 C) is located at the upper left-hand corner, while the second charge (q2 = +2.0 × 10-6 C) is at the lower right-hand corner. Determine the electric potential at the upper right-hand corner of the rectangle.
Solution: To calculate the electric potential, we will sum up the electric charges present in the right-hand corner of the rectangle:
Given :
K = 9 × 10 9 N.m2/c2
q1 = -5 × 10 -6 C
q2 = +2.0 × 10 -6 C
r1 = 0.05m, r2 = 0.15m
V = Σ(kq/r) V = k[(-5×10-6/0.15) + (2×10-6/0.05)]
V = 60000 volts
Problem 5. What is the potential difference for a point at the right-hand corner (call it point A) of the rectangle in question #4 relative to the lower left-hand corner (call it point B)?
Solution: VA = 60000 volts
as the value of the electric potential at the lower left corner is asked
hence here,
r1 = 0.15m, and r2 = 0.05mVB = k[(-5×10-6/0.05) + (2×10-6/0.15)] = -780000 volts
ΔV = VA – VB = 60000 - (-780000) = 840000 volts
Therefore, the Potential difference between points A & B is 840000 V.
Unsolved Problems
Q1. A point charge of +3 μC is located at the origin. Calculate the electric potential at a point 5 meters away from the charge.
Q2. Two point charges, +6°C and −4°C, are placed 2 meters apart in air. Determine the electric potential at a point midway between the charges.
Q3. A uniform electric field of magnitude 200N/C exists in the positive x-direction. Calculate the electric potential difference between two points, A and B, that are 3m apart along the x-axis.
Q4. A charge distribution creates an electric potential of 50 volts at a distance of 4m from the center of the distribution. Determine the total charge of the distribution if it is spherically symmetric.
Q5. A capacitor has a capacitance of 20μF and is connected to a 100V battery. Calculate the electric potential difference across the plates of the capacitor.