$A$ particle of charge $q$ and velocity $v$ passes undeflected through a space with non-zero electric field $E$ and magnetic field $B$. The undeflected condition will hold if:

The magnetic force depends on $v$,which depends on the inertial frame of reference. Does the magnetic force differ from one inertial frame to another? Is it reasonable that the net acceleration has a different value in different frames of reference?

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

The electrostatic force $(\vec{F}_1)$ and magnetic force $(\vec{F}_2)$ acting on a charge $q$ moving with velocity $\vec{v}$ can be written as:

$A$ particle of mass $1 \times 10^{-26} \,kg$ and charge $1.6 \times 10^{-19} \,C$ travelling with a velocity $1.28 \times 10^6 \,ms^{-1}$ along the positive $X$-axis enters a region in which a uniform electric field $E$ and a uniform magnetic field of induction $B$ are present. If $E = -102.4 \times 10^3 \hat{k} \,NC^{-1}$ and $B = 8 \times 10^{-2} \hat{j} \,Wbm^{-2}$, the direction of motion of the particle is: