Question

From which of the following 1Wb/m$^2$ is equal to:
A. ${10^4}G$
B. ${10^2}G$
C. ${10^{ - 2}}G$
D. ${10^{ - 4}}G$

Answer 1

Given, Wb/m$^2$ is the unit of magnetic flux divided by area. We know that magnetic flux is defined as $\phi = BA\cos \theta$, where B is the magnetic density and A is the area enclosed. As $\cos \theta$ is dimensionless, therefore a unit of magnetic flux divided by unit of area gives a unit of magnetic field intensity which is 1T. Then we convert that, 1T$= {10^4}G$.

Complete step by step answer:
Magnetic flux$\left( \phi \right)$ is defined as a dot product of magnetic field intensity(B) and area enclosed (A), $\phi = BA\cos \theta$.
Therefore the dimension of the magnetic field is,
$\left[ B \right] = \dfrac{{\left[ \phi \right]}}{{\left[ {A\cos \theta } \right]}}$.
Here $\cos \theta$ is dimensionless.

In SI unit:
The unit for magnetic flux is Weber (Wb). The unit of area is meter $^2({m^2})$.
We know that, $1\dfrac{{Wb}}{{{m^2}}} = 1T$.
And in CGS units, $1T = {10^4}G$. Where G represents Gauss.

Therefore the 1Wb/m$^2$ is equal to $1T = {10^4}G$.

Additional information:
Faraday’s great insights lay on finding a simple mathematical relation to explain the series of experiments that he conducted on electromagnetic induction. Faraday made numerous contributions to science and is widely known as the greatest experimental scientist of the nineteenth century. Before we start appreciating his work, let us understand the concept of magnetic flux which plays a major part in the electromagnetic induction.

In order to calculate the magnetic flux, we consider the field-line image of a magnet or the system of magnets, as shown in the image below. The magnetic flux through a plane of the area given by A that is placed in a uniform magnetic field of magnitude given by B is given as the scalar product of the magnetic field and the area A.

Note: One should know the standard SI and CGS units of the quantities in the syllabus and the relation between them to solve such a type of problem. Here we use 1Wb/m$^2$ is equal to $1T = {10^4}G$. Moreover,if the magnetic field is non-uniform and at different parts of the surface, the magnetic field is different in magnitude and direction, then the total magnetic flux through the given surface can be given as the summation of the product of all such area elements and their corresponding magnetic field.