$A$ particle with charge-to-mass ratio $\frac{q}{m} = \alpha$ is shot with a speed $v$ towards a wall at a distance $d$,moving perpendicular to the wall. The minimum value of the magnetic field $\vec{B}$ that exists in this region,perpendicular to the velocity of the particle,such that the particle does not hit the wall is:

Which of the following,while in motion,cannot be deflected by a magnetic field?

Given below are two statements:
Statement $I$: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.
Statement $II$: The electric force accelerates the positively charged particle perpendicular to the direction of the electric field. The magnetic force accelerates the moving charged particle along the direction of the magnetic field.
In the light of the above statements,choose the most appropriate answer from the options given below:

The velocity of certain ions that pass undeflected through crossed electric field $E = 7.7 \, kV/m$ and magnetic field $B = 0.14 \, T$ is.....$km/s$

$A$ charged particle of specific charge $\alpha$ is released from the origin at time $t = 0$ with velocity $\vec{V} = V_o \hat{i} + V_o \hat{j}$ in a magnetic field $\vec{B} = B_o \hat{i}$. The coordinates of the particle at time $t = \frac{\pi}{B_o \alpha}$ are (specific charge $\alpha = q/m$):

At $t = 0$,a positively charged particle of mass $m$ is projected from the origin with velocity $u_0$ at an angle $37^o$ from the $x$-axis as shown in the figure. $A$ constant magnetic field $\vec{B_0} = B_0 \hat{j}$ is present in space. After a time interval $t_0$,the velocity of the particle may be: