Question

The unit of charge is coulomb in SI system and esu of charge in C.G.S system. Then, 1 coulomb is equals to
(A). $3\times {{10}^{9}}esu$
(B). $\dfrac{1}{3}\times {{10}^{9}}esu$
(C). $\dfrac{1}{3}\times {{10}^{8}}esu$
(D). $9\times {{10}^{9}}esu$

Answer 1

The coulomb is the SI unit of charge while esu is the CGS unit. SI system of units is a bigger unit while CGS unit is the smaller unit. The charge of a body is the product of current and time taken. So, its unit is ampere-second, we can convert it into CGS to get the answer.

Formula used:
$q=I\times t$

Complete step-by-step solution:
Charge is the property of matter by virtue of which it experiences forces when kept in an electric field.

We know that,
$q=I\times t$ - (1)
Here, $q$ is the charge
$I$ is the current
$t$ is the time taken

The SI unit of charge is coulomb. From the above equation, in SI unit,
$C=A-\sec$
Here, $C$ represents coulomb
$A$ represents ampere, that is the SI unit of current
$\sec$ represents seconds, which is the SI unit of time

The CGS unit of coulomb is esu. Therefore, using eq (1) to represent coulomb in charge in CGS units will be-
$esu=emu-\sec$
Here, $emu$ is the CGS unit of current
$\sec$ is the CGS unit of time.

Therefore,
$1C=3\times {{10}^{9}}esu$

Therefore, 1 coulomb in CGS units is $3\times {{10}^{9}}esu$. Hence, the correct option is (A).

Note:
The CGS unit of current is also known as biot and 10 parts of biot make an ampere. The SI unit system is the most commonly used system in the world and is based on seven fundamental units, while the CGS system is based on using centi-metre as unit of length, gram as unit of mass and seconds as unit of time. When converting from a smaller system of units to a bigger system of units we divide, while if we convert from bigger units to smaller we multiply.