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The equipotential surface is the surface that consists of points having equal potentials. In simpler words, any surface that has the same electric potential at every point is known as an equipotential surface. Points in an electric field that are at the same potential are known as equipotential points and if they are connected by a curve, then it is called an equipotential line. Also, equipotential volume is the distribution of these points all over the space. The most commonly encountered equipotential is a surface.
Electric Potential
Electric Potential of charge ‘q’ is defined as the amount of work done to bring a unit positive charge from infinity to that point. The concept of electric potential is used to express the effect of an electric field of a source in terms of the location within the electric field. The potential energy associated with a charge having twice the quantity of charge will be twice as compared to other charges in a given location but its electric potential would be the same as any other test charge. If we want to increase the electric potential of a positive test charge, then it is to be held closer to the positive source of charge. The farther we move from the source, the magnitude of electric potential keeps on decreasing. From this, we can conclude that electric potential is a property of the location within an electric field. We can also say, an electric potential is a potential energy per unit charge, i.e,
Electric potential = P.E/Q
Properties of Equipotential Surface
The electric field lines point from higher to lower potential and are perpendicular to the given surface.
To move a charge from one point to another, the work done is zero, which, in turn, means the tangential component of the electric field along the equipotential surface has to be zero. Had it not been zero, some amount of work would have always been required to move a charge from one point to another.
The equipotential surface produced by point charges is a family of concentric circles and a constant electric field produces a family of planes that are perpendicular to the given lines.
Equipotential surfaces do not intersect each other.
Work done in moving a charged particle from one point to another is always zero.
Now, we’ll be discussing the fifth property in detail, i.e, work done is always zero on an equipotential surface.
Work done in Equipotential Surface
The work done in moving a charge between two points in an equipotential surface is zero. Let’s consider two points, VA and VB in an equipotential surface. The work done in moving a charge from VA to VB will be given by
W=q0(VA-VB)
The surface being equipotential implies that every point will be at the same potential, i.e, VA-Vb=0
Therefore, the work done will also be zero.
W = 0
Examples
An isolated metallic sphere with uniform distribution of negative charge is an example of an equipotential surface. Why? We are aware of the fact that the electric field lines are always perpendicular to the surface of metal, proving it’s an equipotential surface. The work done in moving a charge between two points in an equipotential surface is zero.
Earth is a good conductor and it has been proved experimentally that at the surface of the earth there is a downward vertical electric field of about 100 V/m all over the earth. The negative surface charge density on the earth is approximately -10-9 C/m2. To sum it up, the earth also acts as an equipotential surface.
Any conductor in an electrostatic scenario can be considered as an equipotential surface. It does not matter whether it’s connected to the ground or not. But you must have observed that electric appliances are grounded. This is done for safety purposes. How? We will discuss that in the next section.
Importance of equipotential surfaces
The difference in the electric potential between two points produces electric current, or simply, a difference in voltages helps the current to flow. We, humans, are bad insulators of electricity. If we accidentally touched a metal surface that is not at the same potential as earth, then current will be produced, which could prove fatal. So, what we do is that we connect electric devices to the earth. This grounding helps in equating the potentials of the earth and any other body which in turn would save us from getting shocked.
Conclusion
Equipotential surfaces are important and we know that point charges give a spherical distribution of equipotential surfaces while charged plates have a planar distribution. Total work done is always zero as the potential difference is zero. The equipotential lines at a given point can have only one value and that’s why they never intersect each other because intersection proves that these lines would have two values at a given point.
