Question

What is the unit of magnetic field?
$\text{A.}\quad H$
$\text{B.}\quad NA^{}m^{-1}$
$\text{C.}\quad NA^{-1}m^{}$
$\text{D.}\quad NA^{-1}m^{-1}$

Answer 1

Hint: Magnetic field is the space around the magnet where the effect of magnet can be felt by another magnet or iron piece. Magnetic fields can also be produced by a moving charge whose intensity can be determined by the velocity and magnitude of charge. The S.I unit of magnetic field is Tesla (T) whereas the C.G.S unit is Gauss (G).

Complete answer:
Note, in the question, we are asked to find the units, in the form in which ‘N’ (Newton)is appearing, hence we have to keep Force as Newton and not to be broken down further. We have so many formulas relating magnetic fields with other quantities. One of which is$F=Bil$. It states that if a current (i) carrying rod of length ‘l’ is moved in a magnetic field, perpendicular to the length of rod, a force ‘F’ acts on the rod which is given by: $F=Bil$

From this equation, we get $B = \dfrac{F}{il}$.

Now, as we know the units of all the terms appearing in the above formula. ‘F’ is the force, having units ‘N’ (Newton). The unit of current is ‘A’ (Ampere) and the unit of length is ‘m’ (meter).
Hence putting the values of units of various terms, we get;
$B = \dfrac{N}{Am} = NA^{-1}m^{-1}$

So, the correct answer is “Option D”.

Note:
There are many more formulas which can be used to get the units of magnetic field. One of them is Biot-Savart's law. But in it, the term $\mu_{\circ}$, which is the permeability of free space, will appear. The units of $\mu_{\circ}$ is $m \ kgs^{-2}A^{-2}$, which is harder to remember. Hence one should keep it as simple as possible. In the question, one more extra unit is given i.e. ‘H’ for confusion. ‘H’ stands for Henry and is the S.I. unit of inductance.