Question

Tesla is the unit of
A. Magnetic flux
B. Magnetic intensity
C. Magnetic induction
D. Magnetic moment

Answer 1

- Hint: Tesla is just another name for the unit $Wb/m^2$ . We need to know which magnetic measurable quantity has this unit. We will also know the relationship between these quantities in order to remember their units easily.

Complete step-by-step solution -
Let’s know that magnetic flux is denoted by $\varphi$, magnetic intensity is denoted by $\overrightarrow{H}$. And,
Magnetic induction=$\overrightarrow{B}$
Magnetic moment=${\overrightarrow{p}}_m$
Now, remember that unit of magnetic flux is Wb (Weber). Mathematically,
$\varphi =\overrightarrow{B}.\overrightarrow{A}$
Here, $\overrightarrow{A}$ is the area and its unit is $m^2$. Plainly, unit of B is given by unit of $\varphi$ divided by unit of area. So, unit of B is $Wb/m^2$.
Hence, $Wb/m^2$ or Tesla is the unit of magnetic induction.
So, option C is the correct answer.

Additional information:
Unit of magnetic intensity is A/m (Ampere per metre).
Unit of magnetic moment is $A.m^2$ (Ampere metre square).
The relationship between all these quantities are as follows,
1. $\varphi =\overrightarrow{B}.\overrightarrow{A}$
2. $\overrightarrow{B}=\mu .\overrightarrow{H}$
3. ${\overrightarrow{p}}_m=I.\overrightarrow{A}$
Here, I= current and $\overrightarrow{A}$ is the areal vector and $\mu$ is called permeability of the medium.
Magnetic flux is basically proportional to the number of magnetic lines of force in a particular given area. It’s a scalar quantity. But, magnetic induction is proportional to the number of lines of force per unit area in a given direction. Hence it is a vector quantity. Magnetic intensity is just the multiplication of magnetic induction and permeability of the medium.
If a circular loop of radius r carries current I, its magnetic moment is given by ${\overrightarrow{p}}_m=I.\pi r^2.\hat{n}$
Here, $\hat{n}$ is the unit vector along the normal to the loop.

Note: It’s advised to remember some units always. Also, never confuse between the magnetic intensity and the magnetic induction. Avoid words like magnetic field in numerical problems, since it’s often used for both of B and H in different text books.