Question

Electric intensity is –
A. a scalar quantity
B. a vector quantity
C. neither scalar nor vector
D. sometimes scalar and sometimes vector

Answer 1

Hint: Electric field is the force experienced by a unit positive charge kept at that point. Relation between electric field intensity E, force F and q is given by $$q\times E=F$$.

Complete step-by-step answer:
Electric field at a point is measured in terms of Electric field intensity or electric intensity E. Electric intensity in an electric field at a point is the force experienced by a unit positive charge kept at that point.
Now, we consider point charge placed at point O in air as shown in figure. A test charge $$q_0$$ is placed at point A at a distance r from point O.

According to Coulomb’s law, the test charge $$q_0$$ experience force F due to point charge q. It is given by,
$$F={\displaystyle \frac{1}{4\pi {\epsilon }_0}}{\displaystyle \frac{q{q}_0}{r^2}}$$ …..(1)
By definition, electric intensity at point B is given as,
$$E={\displaystyle \frac{F}{q_0}}$$ …..(2)
Using equation (1) and (2) we can write,
$$E={\displaystyle \frac{1}{4\pi {\epsilon }_0}}{\displaystyle \frac{q}{r^2}}$$
The direction of F is along the line joining the points O and A, passing away from the charge q if q is positive and toward q, if q is negative. So, the direction is the same as force.
Hence, electric intensity is a vector quantity.
Force in vector form,
$$\overrightarrow{F}={\displaystyle \frac{1}{4\pi {\epsilon }_0}}{\displaystyle \frac{q{q}_0}{{\overrightarrow{r}}^3}}\hat{r}$$
Electric intensity in vector form is,
$$\overrightarrow{E}={\displaystyle \frac{1}{4\pi {\epsilon }_0}}{\displaystyle \frac{q}{{\overrightarrow{r}}^3}}\hat{r}$$
where, $$\overrightarrow{r}$$ is a position vector and $$\hat{r}$$ is a unit vector.

Note: Electric intensity is also known as electric field and electric field intensity. Every charged particle creates an electric field around it in which the effect of electric force is experienced by another charge. The SI unit of electric intensity is Newton per coulomb and dimension is $$\left[ML{T}^{-3}{A}^{-1}\right]$$.