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Derivation of electric potential due to a point charge is?
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Electric Potential due to a point charge
The electric potential due to a point charge at a any point is defined as the work done in bringing per unit (infinitesimal and positive) test charge from infinity to given point. Let q be the charge and P a point at a distance r from q at which the potential is to be found.
Suppose test charge q0 is being brought from infinity to point P . When test charge q0 is at a distance x, the electrostatic coulomb force on the test charge is
where 
is unit vector along 
Work done by external force against electric force during small displacement dx is .
Work done by external force against electric force during small displacement dx is
Work done in bringing test charge q0 from infinity to point P is
The electric potential at point P (distant r from point charge q ) is
Clearly, the potential due to a point charge varies inversely with distance r from the point charge (fig.)
FAQs on Derivation of electric potential due to a point charge is? - Class 12
| 1. What is the formula for the electric potential due to a point charge? |  |
Ans. The formula for the electric potential due to a point charge is V = kQ/r, where V is the electric potential, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), Q is the magnitude of the charge, and r is the distance from the charge to the point where the potential is measured.
| 2. How is the electric potential different from electric field? | |
Ans. The electric potential at a point is a scalar quantity that represents the amount of electric potential energy per unit charge at that point. It is measured in volts (V). On the other hand, the electric field at a point is a vector quantity that represents the force experienced by a positive test charge per unit charge at that point. It is measured in newtons per coulomb (N/C).
| 3. Can the electric potential be negative? | |
Ans. Yes, the electric potential can be negative. The sign of the electric potential depends on the sign of the charge creating the potential. If the charge is positive, the electric potential is positive. If the charge is negative, the electric potential is negative.
| 4. How does the electric potential change with distance from a point charge? | |
Ans. The electric potential due to a point charge decreases as the distance from the charge increases. This relationship follows an inverse-square law, meaning that doubling the distance from the charge will result in a quarter of the original electric potential.
| 5. Can the electric potential due to a point charge ever be zero? | |
Ans. Yes, the electric potential due to a point charge can be zero. This occurs at a point where the distance from the charge is infinity. At this point, the electric potential becomes zero as the distance approaches infinity.
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