A charge particle moving in magnetic field $B$, has the components of velocity along $B$ as well as perpendicular to $B$. The path of the charge particle will be

Which law is useful to determine relation between current and magnetic fields due to it.

Bob of a simple pendulum of length $l$ is made of iron . The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is $T$ then

A proton (mass $m$ and charge $+e$) and an $\alpha  -$ particle (mass $4m$ and charge $+2e$) are projected with the same kinetic energy at right angles to the uniform magnetic field. Which one of the following statements will be true

A magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{j}}$ exists in the region $\mathrm{a} < \mathrm{x} < 2 \mathrm{a}$ and $\vec{B}=-B_0 \hat{j}$, in the region $2 \mathrm{a} < \mathrm{x} < 3 \mathrm{a}$, where $\mathrm{B}_0$ is a positive constant. $\mathrm{A}$ positive point charge moving with a velocity $\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\dot{i}}$, where $v_0$ is a positive constant, enters the magnetic field at $x=a$. The trajectory of the charge in this region can be like,