An electric charge $+q$ moves with velocity $\overrightarrow{V} = 3\hat{i} + 4\hat{j} + \hat{k}$ in an electromagnetic field given by $\overrightarrow{E} = 3\hat{i} + \hat{j} + 2\hat{k}$ and $\overrightarrow{B} = \hat{i} + \hat{j} - 3\hat{k}$. The $y$-component of the force experienced by $+q$ is: (in $q$)

Give the definition of magnetic field and provide its unit.

An electron is moving with a velocity $\vec{v} = (2 \hat{i} + 3 \hat{j}) \text{ m/s}$ in an electric field $\vec{E} = (3 \hat{i} + 6 \hat{j} + 2 \hat{k}) \text{ V/m}$ and a magnetic field $\vec{B} = (2 \hat{j} + 3 \hat{k}) \text{ T}$. Calculate the magnitude and direction (with $x$-axis) of the Lorentz force acting on the electron.

Write the formula for the magnetic force acting on a moving charge $q$ in a magnetic field $B$.

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

$A$ particle having charge $10^{-9} \text{ C}$ moving in the $x-y$ plane in fields of $0.4 \hat{i} \text{ N/C}$ and $4 \times 10^{-3} \hat{k} \text{ T}$ experiences a force of $(4 \hat{i} + 2 \hat{j}) \times 10^{-10} \text{ N}$. The velocity of the particle at that instant is . . . . . . $\text{m/s}$.