Lorentz force can be calculated by using the formula
A. \[\vec F = q\left[ {\vec E + \vec v \times \vec B} \right]\]
B. \[\vec F = q\left[ {\vec E - \vec v \times \vec B} \right]\]
C. \[\vec F = q\left[ {\vec E dot \vec v \times \vec B} \right]\]
D. \[\vec F = q\left[ {\vec E + \vec B + \vec v} \right]\]

Hint: In the given question, we need to find the formula of Lorentz force. For this, we need to use the concept that the Lorentz Force is defined as the force on a charged particle due to electric as well as magnetic fields to get the desired result.



Complete answer:
We know that a charged particle moving at speed \[v\] through an electric field \[E\]and a magnetic field \[B\] experiences the Lorentz force.
Mathematically, it is defined as
\[\vec F = {\vec F_e} + {\vec F_m}\]
Here, \[{\vec F_e}\]is the force vector due to electric field and \[{\vec F_m}\]is the force vector due to magnetic field
But \[{\vec F_e} = q\vec E\] and \[{\vec F_m} = q(\vec v \times \vec B)\]
Here, \[q\] is the charge.
Thus, we get
\[\vec F = q\vec E + q(\vec v \times \vec B)\]
By simplifying, we get
\[\vec F = q\left[ {\vec E + \vec v \times \vec B} \right]\]
Thus, we can say that Lorentx force can be calculated by using the formula \[\vec F = q\left[ {\vec E + \vec v \times \vec B} \right]\].
Therefore, the correct option is (A).

Additional Information : The electromagnetic field-induced magnetic and electric forces acting on a point charge are referred to as the Lorentz force. It is also referred to as the electromagnetic force and it is used in electromagnetism. Hendrik Lorentz developed the present Lorentz force formula in\[1895\]. Also, the physical significance of force applied on charged particles as they travel through space with an electric and magnetic field is explained by Lorentz's force, which also describes the mathematical equations behind them.



Note: Many students make mistakes in writing the formula of the Lorentz force. This is the only way through which we can solve the example in the simplest way. Also, it is essential to analyse the concept of Lorentz force carefully to get the desired result regarding proton and electron.