Question

1 T equals to
${\text{A}}{\text{. 1}}N{A^{ - 1}}{m^{ - 1}} \\\ {\text{B}}{\text{. 1}}N{A^{ - 1}}{m^{ - 2}} \\\ {\text{C}}{\text{. 1}}NA{m^2} \\\ {\text{D}}{\text{. none of these}} \\\$

Answer 1

The SI unit of magnetic field is tesla (T). Based on the units given in the options, we need to obtain the units of magnetic field in terms of units of force, current and length and that is possible if we use the expression for magnetic Lorentz force which relates force with charge, velocity and the magnetic field.

Formula used:
The force experienced by a charge due to magnetic field is given by the Lorentz force law which is given as
$F = qVB\sin \theta$
Here F is the Lorentz force acting on a charged particle which has charge q on it. V is the velocity with which the particle moves and B is the magnetic field acting on the particle.

Complete step by step answer:
Magnetic field can be defined as the field produced due to moving charges. The SI unit of magnetic field is tesla(T).
Now all we need to do is insert the SI units of all the quantities in the expression for Lorentz force. We know that SI unit of force is newton (N), charge is coulomb (C) or ampere second (As) , velocity is metre per second (m/s) while that of magnetic field is tesla (T). Inserting all these values in the Lorentz force law, we obtain the following expression.
$1N = \left( {1As} \right)\left( {1m{s^{ - 1}}} \right)\left( {1T} \right)$
We can rearrange this expression in the following way.
$1N = 1AmT \\\ \Rightarrow 1T = 1N{A^{ - 1}}{m^{ - 1}} \\\$
Hence, the correct answer is option A.

Note:
1. All the units of a quantity must be expressed in the same system of units at a time.
2. There exist many expressions for magnetic fields but in these types of questions, first check the quantities that are being used in the option and then think about which law or expression should be used to obtain the required units.
3. Sine or cosine of an angle is a dimensionless quantity.