An electron is moving along the positive $X$$-$axis. You want to apply a magnetic field for a short time so that the electron may reverse its direction and move parallel to the negative $X$$-$axis. This can be done by applying the magnetic field along

A proton of energy $8\, eV$ is moving in a circular path in a uniform magnetic field. The energy of an alpha particle moving in the same magnetic field and along the same path will be…..$eV$

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement$(s)$ is/are true?

$(A)$ They will never come out of the magnetic field region.

$(B)$ They will come out travelling along parallel paths.

$(C)$ They will come out at the same time.

$(D)$ They will come out at different times.

Two long parallel conductors $S_{1}$ and $S_{2}$ are separated by a distance $10 \,cm$ and carrying currents of $4\, A$ and $2 \,A$ respectively. The conductors are placed along $x$-axis in $X – Y$ plane. There is a point $P$ located between the conductors (as shown in figure).

A charge particle of $3 \pi$ coulomb is passing through the point $P$ with velocity

$\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s$; where $\hat{i}$ and $\hat{j} \quad$ represents unit vector along $x$ and $y$ axis respectively.

The force acting on the charge particle is $4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N$. The value of $x$ is

A particle of charge $q$ and mass $m$ starts moving from the origin under the action of an electric field $\vec E = {E_0}\hat i$ and $\vec B = {B_0}\hat i$ with velocity ${\rm{\vec v}} = {{\rm{v}}_0}\hat j$. The speed of the particle will become $2v_0$ after a time