An electron moves straight inside a charged parallel plate capacitor of uniform charge density $\sigma$. The space between the plates is filled with a uniform magnetic field of intensity $B$,as shown in the figure. Neglecting the effect of gravity,the time taken for the straight-line motion of the electron in the capacitor is:

The current flowing along the path $A B C D$ of a cube (shown in the left figure) produces a magnetic field at the centre of the cube of magnitude $B$. Dashed lines depict the non-conducting part of the cube. Consider a cubical shape shown to the right which is identical in size and shape to the left. If the same current now flows in along the path $D A E F G C D$,then the magnitude of the magnetic field at the centre will be

Two circular coils $1$ and $2$ are made from the same wire,but the radius of the first coil is twice that of the second coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?

If the induction of a magnetic field at a point is $B$ and the energy density is $U$,then which of the following graphs is correct?

$A$ charged particle of mass $m$ and charge $q$ moving under the influence of a uniform electric field $E\hat{i}$ and a uniform magnetic field $B\hat{k}$ follows a trajectory from point $P$ to $Q$ as shown in the figure. The velocities at $P$ and $Q$ are respectively $v\hat{i}$ and $-2v\hat{j}$. Which of the following statements $(A, B, C, D)$ are correct? (Trajectory shown is schematic and not to scale)
$(A)$ $E = \frac{3}{4}\left(\frac{mv^{2}}{qa}\right)$
$(B)$ Rate of work done by the electric field at $P$ is $\frac{3}{4}\left(\frac{mv^{3}}{a}\right)$
$(C)$ Rate of work done by both the fields at $Q$ is zero
$(D)$ The difference between the magnitude of angular momentum of the particle at $P$ and $Q$ is $2mav$.

$A$ particle of charge $+q$ and mass $m$ moving under the influence of a uniform electric field $E\hat i$ and a uniform magnetic field $B\hat k$ follows a trajectory from $P$ to $Q$ as shown in the figure. The velocities at $P$ and $Q$ are $v\hat i$ and $-2v\hat j$ respectively. Which of the following statement$(s)$ is/are correct?