Work Done On Equipotential Surface

An equipotential surface is an area in which all the potential charges of various points are the same. This makes the electrostatic forces that usually act on charges completely null and void, making the charges move freely without any disturbance. Hence, the work done in moving two points in an equipotential surface is zero. The surface of an electric conductor is the best example of an equipotential surface. 

Definition of Equipotential Surface

When the charge at any given point on a surface is equal to every other charge present on the surface, such a surface is called an Equipotential surface or a potential Isosurface. As the name suggests, such surfaces have a set potential charge at all points on them. 

When a charge moving from point A to Point B gains some amount of energy in the movement depending on the type of charge – negative or positive – we calculate the amount of work done in terms of Joules.

The Formula for Equipotential Surfaces

In an electromagnetic field, the charges, while moving from one point to another, have to gain some energy to make this movement happen. This energy is called electrostatic potential energy. However, in the case of an equipotential surface, this work is reduced to nothing as, at this particular point, the potential charges of points become the same. 

The formula used to calculate the magnitude of charge needed to move from point A to Point B is: 

W= q0(VA- VB)

If the equipotential surface has the same charge for all points, the charge on point A will be equal to the charge on Point B, which makes the whole equation sum to a zero.

Characteristics of an Equipotential Surface

The following are the characteristics of an equipotential surface:

• Every equipotential surface has an electromagnetic field that lies at a perfect right angle to its parallel.

• Two equipotential surfaces can never meet.

• There are concentric circles around the central point charge on the equipotential surface when the charge is negative, and when the charge is positive, there are radiating lines from the centre.

• The difference between a strong electromagnetic field and a weak one depends upon the distance between the two equipotential surfaces.

• The potential charges of points remain equal at an equipotential surface, making the work done by the moment of a unit charge equal to zero.

Equatorial Surface

To understand how the wind stress, which is otherwise exerted by the winds, is relaxed at exactly the midpoint of the Earth, we need to understand the theory of Michael Faraday. This theory states that when there is a hollow sphere that repels or blocks the electromagnetic field, it so happens that the middle circumference of the sphere acts as an Equipotential Surface. 

This is why the winds that move or blow from the 30 degrees north and south latitudes towards the equator have reduced the stress of wind, making it possible for the winds to move freely in this region. In an electric conductor, the charges at any given point on its surface remain the same. So is the case with the equatorial regions that lie in the middle of all latitudes covering approximately 6% of the total landmass of the Earth that lay in a band around the equator.  

Conclusion

The work is done to move a positive unit charge from one point to another on an equipotential surface equal to zero. This happens because the most outstanding property of an equipotential surface is that it is the point at which any given point is equal to all the other points that are potentially charged. The work that is done to move a potential charge is completely zero; therefore, the work done also equals zero Joules.