Question

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

Answer 1

Hint:: To find the unit of magnetic field use the formula for the force exerted on a current carrying conductor placed in an external magnetic field. With the help of this formula find the dimensions of the magnetic field and substitute the units of the known quantities.

Formula used:
$\overrightarrow{F}=i\left( \overrightarrow{L}\times \overrightarrow{B} \right)$

Complete answer:
Let us first understand what a magnetic field is. Magnetic field is a property of current or moving charges. A current flowing in a conductor produces magnetic field lines around it.
To find the unit of the magnetic field we use the formula for the force exerted on a current carrying conductor placed in an external magnetic field. When a conductor carrying current is placed in an external magnetic field, a magnetic force is exerted on the conductor.

This magnetic force is given as $\overrightarrow{F}=i\left( \overrightarrow{L}\times \overrightarrow{B} \right)$ …. (i)
Here, $i$ is the current flowing in the conductor, $\overrightarrow{L}$ is the length vector of the conductor and $\overrightarrow{B}$ is the magnetic field.

From (i), we get that the dimensional formula for the magnetic force is,
$\left[ F \right]=\left[ i \right]\left[ L \right]\left[ B \right]$.
Therefore, the dimensional formula of magnetic field is,
$\left[ B \right]=\left[ F \right]{{\left[ i \right]}^{-1}}{{\left[ L \right]}^{-1}}$.
Now we can calculate the MKS unit of magnetic from the above equation.
The unit of current (i) is A. The unit of force (F) is N. The unit of length (L) is m.
Therefore, the unit of magnetic field B is $N{{A}^{-1}}{{m}^{-1}}$.

Hence, the correct option is D.

Note:The SI unit of magnetic field is tesla (T). Therefore $1T=1N{{A}^{-1}}{{m}^{-1}}$.
This is one of the ways to find the unit of magnetic field. We can also use the other formulas involving magnetic fields in them. However, they must know the units of other quantities. H (Henry) is a unit of inductance.