Question

Define electric potential and write down its dimension.

Answer 1

Hint: The formula for electric potential is ${\rm{V}} = \dfrac{{\rm{U}}}{{\rm{q}}}$ and we
can find the dimension of the electric potential from this formula. Electric potential can be said
to be the feature of the electric field.

The electrical energy potential of a charged particle in an electric field depends on the electric
field as well as on the charge of the particle.
The electric potential ${\rm{V}}$is defined as the electric potential energy, ${\rm{U}}$ per
unit charge ${\rm{q}}$.
So, mathematically electric potential could be written as:
${\rm{V}} = \dfrac{{\rm{U}}}{{\rm{q}}}$
The electric potential has only magnitude and no direction. So, it is a scalar quantity.
Everywhere in space the electric potential is known as a quantity, but has no direction.
The electrical potential is same for all charges at a given location.

The electrical potential is likewise characterized as the work required against an electrical field
to move a unit positive charge from an infinite separation to a given point.
The potential at infinity is zero.
Electric potential is also simply known as potential.
The S.I unit of electric potential is joule/coulomb or volts.
The dimensions for electric potential can be found as follows:
${\rm{V}} = \dfrac{{\rm{U}}}{{\rm{q}}}$
The electric potential energy, ${\rm{U}}$ can also be taken as work done ${\rm{W}}$.
Substituting ${\rm{U}}$ with ${\rm{W}}$, we get:
${\rm{V}} = \dfrac{{\rm{U}}}{{\rm{q}}} = \dfrac{{\rm{W}}}{{\rm{q}}} =
\dfrac{{{\rm{F}}{\rm{.d}}}}{{\rm{q}}}$, where work done $ = $force $ \times $distance
$\begin{array}{l}{\rm{V}} = \dfrac{{\rm{U}}}{{\rm{q}}} = \dfrac{{\rm{W}}}{{\rm{q}}} =
\dfrac{{{\rm{F}}{\rm{.d}}}}{{\rm{q}}}\\ \Rightarrow
{\rm{M}}{{\rm{L}}^{\rm{2}}}{{\rm{T}}^{ - 2}}{{\rm{C}}^{ - 1}} =
{\rm{M}}{{\rm{L}}^{\rm{2}}}{{\rm{T}}^{ - 3}}{{\rm{A}}^{ - 1}}\end{array}$
Hence, the dimension for electric potential is ${\rm{M}}{{\rm{L}}^{\rm{2}}}{{\rm{T}}^{ -
3}}{{\rm{A}}^{ - 1}}$.

Note: The electrical potential energy is directly proportional to the charge but electrical potential
is the property of the electrical field itself not depending on the charged particle.