Question

Define one tesla using the expression for the magnetic force acting on a particle of charge ‘q’ moving with velocity $\vec{V}$ in a magnetic field $\vec{B}.$

Answer 1

Hint : In this question, we are required to define one tesla using the expression and in order to do that we will use the formula for magnetic field vectors. A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

Complete step by step answer:
The International System unit of field intensity for magnetic fields is Tesla (T). One Tesla (1T) is defined as the field intensity generating one newton (N) of force per ampere (A) of the current per meter of conductor. Certain other non-SI units, like Gauss (G), are still occasionally used. The magnetic field of one tesla is quite strong. That is why magnetic fields are usually expressed in microtesla$(\mu T)$.
According to the Lorentz force law, when a particle carrying a charge of one coulomb, and moving perpendicularly through a magnetic field of one tesla, at a speed of one meter per second, experiences a force with magnitude one newton.
Using the definition of the cross product, the magnetic force can be written as a scalar equation:
$F=qvB\sin \theta \,\,\,\,.....(1)$
The equation (1) can also be written as:
$B=\dfrac{F}{qv\sin \theta }\,\,\,\,.....(2)$
Where,
$B=$Magnetic field
$F=$Force
$q=$Charge
$v=$Velocity
If$F=1N,\,\,q=1C,\,\,v=1\,m{{s}^{-1}},\,\,\theta ={{90}^{o}},\,$
Then, the SI unit of $B:$
$B=\dfrac{1N}{1C.1\,m{{s}^{-1}}.\sin {{90}^{o}}}$
$B=1N{{A}^{-1}}{{m}^{-1}}=1\,tesla$

Therefore, when a charge of $1C$, moving with velocity $1\,m{{s}^{-1}}$, normal to the magnetic field, experiences a force of $1N$, then the magnetic field is said to be one tesla.

Note: In order to solve this kind of question, we should have knowledge about force, magnetic field properties, and Lorentz force low. Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin.