A proton accelerated by a potential difference $500\;KV$ moves though a transverse magnetic field of $0.51\;T$ as shown in figure. The angle $\theta $through which the proton deviates from the initial direction of its motion is......$^o$

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $\vec{E}=E_0 \hat{j}$ and $\vec{B}=B_0 \hat{j}$. At time $t=0$, this charge has velocity $\nabla$ in the $x$-y plane, making an angle $\theta$ with $x$-axis. Which of the following option$(s)$ is(are) correct for time $t>0$ ?

$(A)$ If $\theta=0^{\circ}$, the charge moves in a circular path in the $x-z$ plane.

$(B)$ If $\theta=0^{\circ}$, the charge undergoes helical motion with constant pitch along the $y$-axis.

$(C)$ If $\theta=10^{\circ}$, the charge undergoes helical motion with its pitch increasing with time, along the $y$-axis.

$(D)$ If $\theta=90^{\circ}$, the charge undergoes linear but accelerated motion along the $y$-axis.

Two ions of masses $4 \,{amu}$ and $16\, amu$ have charges $+2 {e}$ and $+3 {e}$ respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.

$A.$ The electron will experience magnetic force along the axis of the solenoid.

$B.$ The electron will not experience magnetic force.

$C.$ The electron will continue to move along the axis of the solenoid.

$D.$ The electron will be accelerated along the axis of the solenoid.

$E.$ The electron will follow parabolic path-inside the solenoid.

Choose the correct answer from the options given below:

A charged particle enters a magnetic field $H$ with its initial velocity making an angle of $45^\circ $ with $H$. The path of the particle will be

When a proton is released from rest in a room, it starts with an initial acceleration $a_0$ towards west. When it is projected towards north with  a speed $v_0$ it moves with an initial acceleration $3a_0$ toward west. The electric and magnetic fields in the room are