$A$ proton is projected with velocity $\overrightarrow{V} = 2 \hat{i} \; m/s$ in a region where magnetic field $\overrightarrow{B} = (\hat{i} + 3 \hat{j} + 4 \hat{k}) \; \mu T$ and electric field $\overrightarrow{E} = 10 \hat{i} \; \mu V/m$. Find the net acceleration of the proton (in $m/s^2$).

$A$ proton moves with a velocity of $5 \times 10^6 \hat{j} \text{ ms}^{-1}$ through a uniform electric field $\vec{E} = 4 \times 10^6 [2 \hat{i} + 0.2 \hat{j} + 0.1 \hat{k}] \text{ Vm}^{-1}$ and a uniform magnetic field $\vec{B} = 0.2 [\hat{i} + 0.2 \hat{j} + \hat{k}] \text{ T}$. The approximate net force acting on the proton is

An electron enters a region where magnetic $(B)$ and electric $(E)$ fields are mutually perpendicular to one another,then

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:

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?

If the magnetic field is parallel to the positive $y$-axis and the charged particle is moving along the positive $x$-axis (Figure),which way would the Lorentz force be for
$(a)$ an electron (negative charge),
$(b)$ a proton (positive charge).