Define electric field intensity. Is it a vector or scalar quantity? Give S.I. unit and dimensional formula of electric field intensity.
Electric Field Intensity: The electric field intensity due to a static point charge at any point in its electric field is defined as the force experienced by a unit positive charge (i.e., test charge) placed at that point.
Let a test charge $q_0$ be placed at a point P in the electric field of the static point charge Q. If $\vec{F}$ is the force experienced by the test charge $q_0$ in the electric field of the point charge, then electric field intensity of the point charge at point P is given by
$\vec{E} = \frac{\vec{F}}{q_0} ...(1)$
where $q_0 \rightarrow 0$ (i.e., $q_0$ is infinitesimally small) so that presence of this charge may not disturb the location of the point source charge producing the electric field. . Hence, expression for electric field intensity can be written as
$\vec{E} = \underset{q_0 \to 0}{\text{Limit}} \frac{\vec{F}}{q_0} ...(2)$
Electric field intensity is a vector quantity because it has both magnitude and specified direction.}
The direction of electric field intensity is the direction in which a unit positive charge (i.e. test charge) would move in the electric field if free to do so.}
SI unit of electric field intensity is newton/coulomb (N C$^{-1}$).
The dimensional formula of electric field intensity, [E] = $\frac{[F]}{[q]} = \frac{[F]}{[It]}$
$[E]= \frac{[MLT^{-2}]}{[AT]} = [MLT^{-3}A^{-1}]$.