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In addition to the revision notes for Electric Potential on this page, you can also access the following Electrostatics learning resources for Electric Potential
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 14.5 | Electric Potential |
In these revision notes for Electric Potential, we cover the following key points:
Electric potential is defined as the electric potential energy per unit charge. It is independent from the test charge.
The formula of electric potential in terms of charge Q and distance r is
The unit of electric potential is Volt, V. From the formula derived from definition of electric potential, it is easy to conclude that
Positive charges placed inside an electric field move from places with higher potential to places with lower potential while negative charges move in the opposite direction. As a result, a potential difference ΔV is produced. It indicates that a movement of electric charges does exist in that specific region.
Potential difference between two points is defined as the work done by external forces on a positive charge to move it from the initial to the final position.
In other words, potential difference is the work per unit charge (or the change in potential energy per unit charge).
When a positive charge moves in the direction of electric field, the electric forces do positive work. As a result, the electric potential energy of the positive charge decreases. This is similar to when a mass is falling from a height h. In this case, the gravity does positive work and therefore, the gravitational potential energy decreases. On the other hand, when a force is exerted in the opposite direction of field lines, some work must be done by an external force against the electric field, which brings an increase in the electric potential energy of the charge, This is similar to when we lift an object upwards at a height h, in which we increase the gravitational potential energy of the object by doing work against gravity on it.
Whatever type of electric field we may consider - whether uniform or non-uniform - there exist some regions in these fields that have the same potential. For example, all points that have the same distance from any of plates in an electric field produced by two parallel plated charged oppositely, have the same potential,
The same thing occurs when the electric field is produced by a point or a spherical charge as well. All points that have the same distance from the point charge or the centre of sphere, have the same potential (are equipotential). In this way, an infinite number of concentric spheres whose surfaces are equipotential does result.
Electric potential produced by a number n of charged spheres when they are connected through conducting wires is
For an individual charged sphere of radius R, the potential inside the sphere is
The potential for points outside the sphere is
where r > R is the distance from the centre of sphere to the given point.
A charge Q experiences an electric force Fe when it is inserted inside an electric field. As a result, it experiences an acceleration a, which based on the Newton's Second Law is
where m is the mass of the charged particle.
When the charged object is quite heavy, the gravitational force cannot be neglected. As a result, there is a combination of two forces, electric and gravitational, which determine the trajectory of the charge moving inside a uniform field.
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