Dimension Formula of Electric Potential and its Derivation

Dimension Formula of Electric Potential: Electric Potential is the amount of Work needed to be done on a unit charge to move it from one point in an electric field to another. The Dimension of Electric Potential is 

M1L2T -3I -1

 The formula expressing Electric Potential is as follows

Electric Potential~(V)~=~{Work~Done~(W)}/{Charge~(q)}

Dimension Formula of Electric Potential

This article provides you Dimension of Electric Potential and its derivation.

Dimension Formula of Electric Potential and Its Derivation

As mentioned above

Electric Potential(V)~=~{Work~Done~(W)}/{Charge~(q)}

Hence

The Dimension of Work Done is calculated as follows:

Work~Done~(W)~=~Force~*~Distance

Also See

Dimension of Electric FieldDimension of Surface Tension
Dimension of Speed of LightDimension of Wavelength

To find the Dimension of Force:

Acceleration~=~{Change~In~Velocity}/{Time~Period}

Hence

Dimension~of~Acceleration~=~{Dimesion~of~Velocity}/{Dimesion~of~Time}

=~{M^0L^1T^{-1}}/{M^0L^0T^1}

=~M^0L^1T^{-2}

Now,

Force~=Mass~*~Acceleration

Dimension~of~Force~=~Dimension~of~Mass~*~Dimension~of~Acceleration

=~M^1L^0T^0~*~M^0L^1T^{-2}

=~M^1L^1T^{-2}

Now,

Dimension~of~Work~Done~(W)~=~Dimension~of~Force~*~Dimension~of~Distance

=~M^1L^1T^{-2}~*~M^0L^1T^0

=~M^1L^2T^{-2}

Now

Dimension~of~Electric~Potential~(V)~=~{Dimension~of~Work~Done~(W)}/{Dimension~of~Charge~(q)}

=~{M^1L^2T^{-2}}/{M^0L^0T^1I^1}

Hence

Dimension~of~Electric~Potential~(V)~=~M^1L^2T^{-3}I^{-1}

What is Electric Potential

The Electric Potential is defined as the work or energy required to move one unit of charge from a reference point to a particular point in an Electric Field. It is denoted as V. However, a definition does not explain anything. To have a deep understanding of Electric Potential, a student must understand what charge and electric field are.

What is Electric Charge

An electric charge is a basic property of sub-atomic particles of a substance which influence or experience a force when moved in an electric or magnetic field. In other words, it is the property of a matter that requires additional force to move in an electric field. Depending on the charge (i.e., whether it is positive or negative), the force required can be in the opposite direction. It’s unit is the Coulomb (C). Sometimes, especially in electrical engineering, the unit used for the measurement of charge is an ampere-hour.

A matter receives a charge from either electrons or protons. Electrons are negatively charged (-1.602×10−19 C) whereas protons are equally but positively charged (i.e. 1.602×10−19 C). Charge. An atom is neutral in nature, i.e. it has an equal number of protons and electrons. If an atom loses an electron, the number of protons in the atom exceeds the number of electrons. Thus, it becomes a cation. If it gains an electron, the number of electrons exceeds the number of protons and becomes an anion.

A charged body has some basic properties

  1. A charged body always repels a similarly charged body, i.e., a positive charge will always repel a positive charge and a negative charge will always repel a negative charge.
  2. A charged body will always attract an oppositely charged body, i.e., a negatively charged body and a positively charged body will always attract each other.
  3. A Charge can never be created or destroyed in a system. It can only be moved or transferred from one place to another. This is known as the Law of Conservation of Charge.
  4. When a charge moves in space, it produces a magnetic field.
  5. Only matter with mass can have a charge. This is because the charge is acquired due to the loss or gain of electrons, which can only be possible with matter with mass.
  6. Charge is quantized. This means that all charges in the world are in the multiple of the basic elementary charge of an electron which is 1.602×10−19 C.
  7. All electrically charged bodies create an electric field around them, the strength of which depends upon the distance from the charge and the value of the charge.

What is an Electric Field

As mentioned above, an Electric Field is a field that forms around a charged body and exerts electric push or pull on other charged bodies present in that field. It is denoted as E. Coulomb’s law governs the force exerted by the two charges in an electric field. Although it is a field, the Electric Field is defined in terms of force. 

Electric Potential

The potential is the energy stored in an object due to some or the other property. For instance, the gravitational potential is the energy stored in an object held above the ground that is not yet materialised. It will materialise only when the object is released. Similarly, electric potential is the energy of attraction or repulsion of a charged body that is not yet materialised. This stored energy can only be there when the charge is placed in an electric field other than its own.

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