Question

Draw a plot showing the variation of
(i) electric field $(E)$
(ii) electric potential $(V)$
with a distance $r$ due to a point charge $Q$.

Answer 1

Hint: We know that intensity of electric field at any point is inversely proportional to the square of distance from the point charge while the electric potential is inversely proportional to the distance from that point. So, for the electric potential the curve is hyperbolic and also for electric field graphs are hyperbolic.

Complete step by step answer:
According to the formula of electric field intensity for a point charge i.e. $E=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\dfrac{Q}{{{r}^{2}}}$. In this formula we can saw that electric field is inversely proportional to the square of distance from the point charge
$\Rightarrow E\propto \dfrac{1}{{{r}^{2}}}$
So, the graph for that has two asymptotes of coordinate axis.
And according to the formula of electric potential for a point charge i.e. $V=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\dfrac{Q}{r}$. In this formula we can see that electric potential is inversely proportional to the distance from the point from the point charge.
  $\Rightarrow E\propto \dfrac{1}{r}$
So, the graph will be a hyperbola with coordinate axis as two asymptotes.

Additional Information: An electric field is a field or space around an electrically charged object where any other electrically charged object will experience a force. The electric field concept arose in an effort to explain action-at-a-distance forces. Electric field intensity is the measure of intensity or strength of electrical force per unit charge at any given point in the electric field.
Electrical potential at a point in an electric field is defined as the amount of work to be done to bring a unit positive electric charge from infinity to that point.

Note: We have to remember the formulae of electric fields in many cases to make the conclusion faster. We can also say the electric field is a measure of force per unit charge; the electric potential is a measure of energy per unit charge. We can also say that due to differences in electric fields an electrical potential difference is developed between the points.