Electric potential
Electric Potential
Electric potential is a fundamental concept in electrostatics and is a measure of the potential energy per unit charge at a point in an electric field. It is a scalar quantity and is represented by the symbol ( V ). The electric potential at a point is defined as the work done by an external force in bringing a unit positive charge from infinity to that point without any acceleration.
Understanding Electric Potential
To understand electric potential, we must first understand electric potential energy. Electric potential energy (( U )) is the energy that a charge possesses due to its position in an electric field. When a charge moves in an electric field, work is done either by or against the field, and this work is stored as potential energy.
The electric potential (( V )) at a point is the electric potential energy (( U )) per unit charge (( q )):
[ V = \frac{U}{q} ]
The unit of electric potential is the volt (V), where 1 volt = 1 joule/coulomb (1 V = 1 J/C).
Electric Potential due to a Point Charge
The electric potential ( V ) at a distance ( r ) from a point charge ( Q ) is given by the formula:
[ V = \frac{kQ}{r} ]
where ( k ) is Coulomb's constant (( k \approx 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 )).
Differences between Electric Potential and Electric Field
| Electric Potential (V) | Electric Field (E) |
|---|---|
| Scalar quantity | Vector quantity |
| Measured in volts (V) | Measured in newtons per coulomb (N/C) or volts per meter (V/m) |
| Does not have direction | Has direction, indicating the force on a positive charge |
| Work done per unit charge | Force per unit charge |
| Independent of the test charge | Dependent on the test charge |
Examples to Explain Electric Potential
Example 1: Calculating Electric Potential from a Point Charge
Calculate the electric potential 0.1 meters away from a point charge of ( 2 \times 10^{-6} ) coulombs.
Using the formula for electric potential due to a point charge:
[ V = \frac{kQ}{r} ]
[ V = \frac{(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2)(2 \times 10^{-6} \, \text{C})}{0.1 \, \text{m}} ]
[ V = \frac{(8.99 \times 10^9)(2 \times 10^{-6})}{0.1} ]
[ V = 179.8 \, \text{V} ]
Example 2: Work Done in Moving a Charge
How much work is done in moving a 1 C charge from a point A to point B if the electric potential at A is 10 V and at B is 5 V?
The work done ( W ) is equal to the charge ( q ) multiplied by the difference in electric potential (( \Delta V )):
[ W = q \Delta V ]
[ W = 1 \, \text{C} \times (10 \, \text{V} - 5 \, \text{V}) ]
[ W = 1 \, \text{C} \times 5 \, \text{V} ]
[ W = 5 \, \text{J} ]
The work done is 5 joules.
Example 3: Electric Potential Energy
What is the electric potential energy of a system where a charge of ( 3 \times 10^{-6} ) C is at a potential of 200 V?
Using the relationship between electric potential and potential energy:
[ U = qV ]
[ U = (3 \times 10^{-6} \, \text{C})(200 \, \text{V}) ]
[ U = 0.0006 \, \text{J} ]
[ U = 600 \, \text{µJ} ]
The electric potential energy of the system is 600 microjoules.
Conclusion
Electric potential is a crucial concept in understanding how charges interact within an electric field. It is related to the potential energy of a charge and is a measure of the work done to move a charge within an electric field. The examples provided illustrate how to calculate electric potential, work done, and potential energy in various scenarios, which are essential for solving problems related to electrostatics in exams.