Question

The value of one farad in e.s.u is:
A. $$3\times {10}^{10}$$
B. $$9\times {10}^{11}$$
C. $${\displaystyle \frac{1}{9}}\times {10}^{-11}$$
D. $${\displaystyle \frac{1}{3}}\times {10}^{-10}$$

Answer 1

Hint: First of all, we will find the relation of one e.s.u in farads. After that we can easily find the one farad in e.s.u. equivalent. We know that one farad is a huge amount of charge.

Complete step by step answer:
In the given question, we are supplied with the following data;
There is charge given whose magnitude is given as one farad.We are required to write its equivalent in e.s.u.

To begin with, let us discuss a bit about e.s.u or electrostatic charge. In the CGS (centimetre-gram-second) system of units, the e.s.u. or electrostatic unit is a unit of charge, and is not the preferred one for use today - rather, in principle, the SI (International System) is preferred, but sometimes many other systems are used in a ‘scientific measurement muddle.’ That said, CGS, particularly with electromagnetics, still has its charm.
One e.s.u. is classified as a charge, so that they exert $$1$$ dyne of force on each other when two such charges are placed $$1\text{cm}$$ apart. To accelerate one gram by $$1\text{cm}{\text{s}}^{-2}$$ , one dyne is equal to the force required.

We know.One e.s.u is equal to $$1.11\times {10}^{-12}$$ farad
So, one farad is equivalent to e.s.u as:
$$\begin{gathered} {\displaystyle \frac{1}{1.11\times {10}^{-12}}} \\ \Rightarrow 9.009\times {10}^{11} \end{gathered}$$
$$\therefore \sim 9\times {10}^{11}$$ e.s.u.

The correct option is B.

Note:While solving this problem, it is important to remember that one fears a huge amount of charge. One farad capacitor is literally not possible, because to store a charge equivalent to one farad, we will need a sphere whose radius is thousands of meters. The capacitance of a capacitor is one farad when a coulomb of electricity can change the potential difference between the two plates of a capacitor by one volt.