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

If two protons are moving with speed $v=4.5 \times 10^{5} \,m / s$ parallel to each other then the ratio of electrostatic and magnetic force between them

If a proton is projected in a direction perpendicular to a uniform magnetic field with velocity $v$ and an electron is projected along the lines of force, what will happen to proton and electron

Two identical charged particles enter a uniform magnetic field with same speed but at angles $30^o$ and $60^o$ with field. Let $a, b$ and $c$ be the ratio of their time periods, radii and pitches of the helical paths than

An electron emitted by a heated cathode and accelerated through a potential difference of $ 2.0 \;kV$, enters a region with uniform magnetic field of $0.15\; T$. Determine the trajectory of the electron if the field

$(a)$ is transverse to its initial velocity,

$(b)$ makes an angle of $30^o$ with the initial velocity

At $t = 0$ a charge $q$ is at the origin and moving in the $y-$ direction with velocity $\overrightarrow v  = v\,\hat j .$ The charge moves in a magnetic field that is for $y > 0$ out of page and given by $B_1 \hat z$ and for $y < 0$ into the page and given $-B_2 \hat z .$ The charge's subsequent trajectory is shown in the sketch. From this information, we can deduce that