Equipotential Surface

What is Equipotential Surface?

The surface that is the locus of all factors that are on the identical capacity is called the equipotential surface. No paintings are needed to transport a fee from one factor to some other at the equipotential surface. In different words, any surface with the identical electric powered capacity at each factor is named an equipotential surface. Any surface over which the capacity is consistent is known as an equipotential surface. In different words, the capacity distinction among any factors on an equipotential surface is zero.

In different terms, an equipotential surface is a surface that exists with an identical electric capacity at every factor. If any factor lies on the identical distance from the difference, then the sum of all factors wilan create an allotted area or a volume. Scientists have termed it as equipotential volume

Define Equipotential Surface

 In different terms, an equipotential surface is a surface that exists with an identical electric capacity at every factor. If any factor lies on the identical distance from the difference, then the sum of all factors wilan create an allotted area or a volume. Scientists have termed it as equipotential volume.

Do you understand the potential executed on an equipotential surface? Well, now it’s time to understand the truth. Let’s recollect that VA and VB each are value of potential on two points on an equipotential surface. We want to calculate the paintings executed withinside the transferring fee. The relation is given below:

W = q0(VA –VB)

However, on an equipotential surface, you’ll discover the distinction among giant factors is zero.

That manner VA –VB = 0 So,

paintings executed = 0

Equipotential Points:

 If the factors in an electric-powered subject are all on the identical electric-powered capacity, then they’re called the equipotential factors. If those factors are linked via the means of a line or a curve, it’s miles called an equipotential line. If such factors lie on a surface, it’s miles known as an equipotential surface. Further, if those factors are allotted for the duration of an area or a volume, it’s miles called an equipotential volume.

Work Done in Equipotential Surface

The paintings performed in transferring a price among factors in an equipotential surface is zero. If a factor price is moved from factor VA to VB, in an equipotential surface, then the paintings performed in transferring the price is given by

W = q0(VA –VB)

As VA – VB is identical to zero, the entire painting performed is W = 0.

Example of Equipotential Surface

• The surface of a charged sphere is an equipotential surface.
• Any imaginary round surface round a factor price is an equipotential surface.
• All the round aircraft surfaces perpendicular to an electric powered dipole and on the center of the dipole are equipotential surfaces
• All of those factors have identical abilities. For example, the surface of a conductor in electrostatics is an equipotential surface. In a pressure subject, the traces of pressure are ordinary, or perpendicular, to an equipotential surface.

An equipotential surface is an actual or imaginary surface having the identical electric

powered ability at each factor on it. Electric subject traces intersect equipotential surfaces perpendicularly in a uniform

electric powered subject. That approach means equipotential surfaces are perpendicular to the uniform electric powered subject. There isn’t any ability distinction among any factors at the equipotential surface. So, no paintings are to be performed to

transport a price from one factor to any other factor at the equipotential surface. The surface of a charged conductor is an equipotential surface.

Numericals on an equipotential surface:

After defining the equipotential surface, let us have a look at the top problems on it:

1. Calculate the work done by the field in moving a charged particle of 1.4 mC to 0.4m in an equipotential surface of 10V.

If the charge is moved in an equipotential surface, the work done in moving the 1.4 mC charge to 0.4m in a 10V surface is zero. All points in an equipotential surface are at the same potential.

2. Calculate the distance traveled by the positive charge of 1.0C that started from the rest on an equipotential surface of 50V, and after the 0.0002s, it is on the equipotential surface of 10V.

Here, q= 1.0C

W= 10V-50V= 40J

Hence, W= q*Ed

40= q*Ed

40= (1.0) * (100)* d

Hence, d= 0.4m

Thus, the distance traveled by the charge is 0.4m.

3. There are two 1.0C charges- one positive and one negative resting in a coordinate system with axis (1.0m, 1.0m), (1.0m, 2.0m). Calculate the potential magnitude on the equipotential surface created by the points at coordinates (1.0m, 1.5m) and (1.5m, 1.5m).

Going through the coordinates of the charges, both positions are equidistant for positive and negative charges. So, the potential is zero as the charges are equal and opposite at both points.

Further, the surface formed by these opposite charges is a plane that passes the system, and any addition of the kq/r for any charge keeps it zero at all times. Further, any points on the equipotential surface are at zero potential irrespective of the coordinates.

Conclusion

An equipotential surface is an actual or imaginary surface having identical electric powered ability at each factor on it. Electric subject traces intersect equipotential surfaces perpendicularly in a uniform electric powered subject. That approach means equipotential surfaces are perpendicular to the uniform electric powered subject.

An equipotential surface is an actual or imaginary surface having the identical electric powered ability at each factor on it.