Question

The SI unit of Magnetic flux is weber and its CGS unit is Maxwell. Then 1 Wb =:
(A). 106 Maxwell
(B). 107 Maxwell
(C). 108 Maxwell
(D). 109 Maxwell

Answer 1

Hint – Magnetic flux is the product of magnetic field and area, so 1 Wb = $\text{Tesla (T)}\times {m^2}$. Here convert the magnetic field and $m^2$ in the CGS unit.
Formula used – $1Wb = Tesla(T) \times {m^2}$.

Complete step-by-step solution -
We have been given that the SI unit of Magnetic flux is Weber and its CGS unit is Maxwell.
Now, we know that the Magnetic flux is the product of magnetic field and area.
Unit of magnetic field is T and the area is $m^2$.
As we have been given that the SI unit of Magnetic flux is Weber, so we can write-
$1Wb = Tesla(T) \times {m^2}$
Also, $1T = {10^4}gauss$ and $1{m^2} = {10^4}{{cm}^2}$
So, T is the SI unit of magnetic field and gauss is the CGS unit of magnetic field.
Similarly, m is the SI unit and cm is the CGS unit of length or distance.
So, converting T into gauss and m into cm, so that we can have the CGS unit of magnetic flux i.e., Maxwell.
So, we can write $1Wb = Tesla(T) \times {m^2}$ as-
$1Wb = {10^4}gauss \times {10^4}c{m^2} = {10^8}$ Maxwell
Hence, the correct option is C.

Note – Whenever such types of questions appear, write down the formula of the magnetic flux as mentioned in the solution. Then, convert into a CGS unit from SI unit. We know the relation that $1T = {10^4}gauss$ and $1{m^2} = {10^4}{{cm}^2}$, so using this we can convert SI unit into CGS unit and then we have found out 1 Wb = 108 Maxwell.