Question

What is the unit of magnetic field ?

• A. H
• B. N A m${}^{-1}$
• C. N A${}^{-1}$ m
• D. N A${}^{-1}$ m${}^{-1}$

Answer 1

The correct option is D N A${}^{-1}$ m${}^{-1}$

The magnitude of the magnetic force $F$ on a charge $q$ moving at a speed $v$ in a magnetic field of strength $B$ is given by

$F=q\times v\times B\times sin\left(\theta \right)$
where, $\theta$ is the angle between the directions of $v$ and $B$. This formula is used to define the magnetic strength $B$ in terms of the force on a charged particle moving in a magnetic field. The S.I. unit for magnitude of the magnetic field strength is called the Tesla $\left(T\right)$ in honor of the brilliant and eccentric inventor Nikola Tesla (1856-1943), who made great contributions to our understanding of magnetic fields and their practical applications. To determine how the Tesla relates to other SI units, we solve $F=q\times v\times B\times sin\left(\theta \right)$ for B.
Magnetic field B is given as $B=\frac{F}{q\times v\times sin\left(\theta \right)}$
Because sin is unitless, the magnetic field unit tesla is
$T=\frac{N}{C\times m{s}^{-1}}$
unit of current $A=\frac{C}{s}$
where, N is Newton, the unit of force, C is Columb, the unit of electric charge and m/s is the unit of speed v. Hence, the unit of magnetic field is given as Tesla (T) which is equal to $N{A}^{-1}{m}^{-1}$