Dimensional Formula of Electric Potential

Potential is an essential concept of mechanics. It can be defined for any force field like a gravitational field, electrostatic field, etc. In this note of the Dimension formula for Electric Potential, we will discuss Potential for the electrostatic field.

Electric Potential is nothing but the work required to bring a charged particle from infinity to the point of reference. We must keep in mind that the acceleration of that point charge should be zero. When a positive direction is brought into a field, a repulsion occurs. The work done against that repulsive force gets stored as potential energy.

Meaning of Electric potential/ Definition:

A point continually defines Electric Potential. To that point, the amount of work is required to bring a positive unit charge from infinity (where the electric field is considered to have zero influence). This is called the Potential of that point. The Potential of the point w.r.t, which is measured, is taken as zero. 

For a point charge, the potential is defined as follows-

V = k. q/r

Formula and Unit of electric Potential:

Electric Potential = Work Done / Unit Charge

Electric Potential in SI units:

V = W/q = Joules/ coulomb = Volts

Electric Potential is thus measured in Volts or Voltage.

1 Volt = 1 Joule/ 1 coulomb

One volt means, for one coulomb of electricity to move, one joule of work must be performed.

Electric Potential is a scalar quantity as we only measure the amount of work done. No directional property is associated with it.

Importance of Electric Potential:

1. The concept of electric potential is associated with the energy of that field.
2. An electric potential difference is measured for all electrical instruments in our regular life, and based on that entire electric supply system works.
3. From the concept of potential energy, we get to know about the existence of equipotential planes.

Dimensional Formula:

The dimensional formula of any bodily amount is defined as the expression that represents how and which of the bottom portions are protected in that amount. It is denoted through enclosing the symbols for base portions with suitable strength in rectangular brackets, i.e. [].

An example is the dimension formula of mass which is given as [M].

Dimensional Formula of Electric Potential

According to the above definition, we can define electric Potential as:

V= W/q

q = electric charge

W = work done

So, dimension of electric potential= dimension of work done / dimension of electric charge.

W= F.S

So, the dimension of W = [MLT-2]x[L] = [ML2T-2]

So, the dimension of V = [ML2T-2]/ [IT] = [MI-1L2T-3]

So, the dimension of Electric potential is [MI-1L2T-3]

Electric Potential for multiple charges:

By the superposition principle, the Electric Potential for point charges can be defined as:

V = Kq/ r

Where: V is the electric potential produced by a point charge with a charge of magnitude Q; r is the distance from the point charge, and k is a constant with a value of 8.99 x 109 N m2/C2.

On account of 3 Charges:

If three charges q1, q2, and q3 are arranged at the vertices of a triangle, the expected energy of the framework is:

U =U12 + U23 + U31 = (1/4πε0) × [q1q2/d1 + q2q3/d2 + q3q1/d3]

On account of 4 Charges:

If four charges q1, q2, q3, and q4 are arranged at the sides of a square, the likely electric energy of the framework is:

U = (1/4πε0) × [(q1q2/d) + (q2q3/d) + (q3q4/d) + (q4q1/d) + (q4q2/√2d) + (q3q1/√2d)]

Unique Case:

In the field of a charge Q, assuming a charge q is moved against the electric field from a distance ‘a’ to a distance ‘b’ from Q, the work done is given by:

W = (Vb – Va) × q

     = [(1/4πε0) × (Qq/b)] – [(1/4πε0) × (Qq/a)]

     = (Qq/4πε0)[1/b – 1/a]

     = (Qq/4πε0)[(a-b)/ab]

Dimensional analysis

In a physical relation, the dimensions are examined through dimensional analysis. These analyses can be used in conversion, correction, and derivation.

Applications of dimensional analysis

It determines the dimensional consistency, homogeneity, and accuracy of the mathematical expressions.

Limitations of the dimensional equation

• The principle of homogeneity of dimensions cannot be used for trigonometric and exponential expressions. The derivation is more complex and complicated.
• The comparing terms or factors are less.
• The correctness of the physical expressions depends only on dimensional equality.
• It is majorly used in the case of dimensional constants. We are not able to find the value of the dimensionless constant.

Conclusion:

In these notes of the Dimension formula for Electric Potential, we learned how to deduce a dimensional formula for Electric Potential and some basic concepts regarding this.

V = kQ/r is the electric potential of a point charge. The difference between a scalar and a vector is the electric Potential. The total electric potential is obtained by adding the voltages as numbers, whereas the entire electric field is obtained by adding the individual areas as vectors. I hope now you have all the necessary information related to this topic. For better understanding, you must go through this topic thoroughly.