$A$ charge $q$ moves with velocity $\vec{V}$ through an electric field $\vec{E}$ as well as a magnetic field $\vec{B}$. Then the force acting on it is:

$A$ charge $q$ moves in a region where both an electric field and a magnetic field exist. The total force on it is:

If a charged particle moves unaccelerated through a region containing both electric and magnetic fields,which of the following must be true?

An electron enters an electric field with intensity $\vec{E} = 3\hat{i} + 6\hat{j} + 2\hat{k} \text{ V m}^{-1}$ and a magnetic field with induction $\vec{B} = 2\hat{i} + 3\hat{j} \text{ T}$ with a velocity $\vec{v} = 2\hat{i} + 3\hat{j} \text{ m s}^{-1}$. The magnitude of the force acting on the electron is (Given, $e = -1.6 \times 10^{-19} \text{ C}$)

In the product $\overrightarrow{F} = q(\vec{v} \times \overrightarrow{B})$ where $\overrightarrow{B} = B \hat{i} + B \hat{j} + B_{0} \hat{k}$. Given $q = 1$,$\vec{v} = 2 \hat{i} + 4 \hat{j} + 6 \hat{k}$,and $\overrightarrow{F} = 4 \hat{i} - 20 \hat{j} + 12 \hat{k}$,what is the complete expression for $\overrightarrow{B}$?

Write the equation for the Lorentz force.