Exercise-2

Two large conducting current planes perpendicular to $x$-axis are placed at $\left(d, 0\right)$ and $\left(2d, 0\right)$ as shown in figure. Current per unit width in both the planes is same and current is flowing in the outward direction. The variation of magnetic induction as function of '$x$' $\left(0\le x\le 3d\right)$ is best represented by -

An electron experiences a force $\left[\left(4.0\hat{\mathrm{i}}+3.0\hat{\mathrm{j}}\right)\times {\mathrm{10}}^{-13}\right] \mathrm{N}$, in a uniform magnetic field when its velocity is $\left[\left(2.5\times {\mathrm{10}}^7\right)\hat{\mathrm{k}}\right] \mathrm{m} {\mathrm{s}}^{-1}$. When the velocity is redirected and becomes $\left[\left(1.5\hat{\mathrm{i}}-2.0\hat{\mathrm{j}}\right)\times {\mathrm{10}}^7\right] \mathrm{m} {\mathrm{s}}^{-1}$, the magnetic force of the electron is zero. The magnetic field vector $\overrightarrow{\mathit{B}}$ is:

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

A particle of specified charge $\left(q/m\right)$ is projected from the origin of coordinates with initial velocity $\left[u\widehat{\mathrm{i}}-v\widehat{\mathrm{j}}\right]$. Uniform electric magnetic fields exists in the region along the $+y$ direction, of magnitude $E$ and $B$. The particle will definitely return to the origin once fi

A particle having charge $q$ enters a region of uniform magnetic field $\overrightarrow{B}$ (directed inwards) and is deflected a distance $x$ after travelling a distance $y$. The magnitude of the momentum of the particle is

A particle moving with velocity $v$ having specific charge $\left(q/m\right)$ enters a region of magnetic field $B$ having width $d=\frac{3mv}{5qB}$ at angle ${53}^{\circ }$ to the boundary of magnetic field. Find the angle $\theta$ in the diagram.

A charged particle enters a uniform magnetic field perpendicular to its initial direction travelling in air. The path of the particle is seen to follow the path in figure. Which of statements $1-3$ is/are correct?

(1) The magnetic field strength may have been increased while the particle was travelling in air
(2) The particle lost energy by ionising the air
(3) The particle lost charge by ionising the air

A semi circular current carrying wire having radius $R$ is placed in $x-y$ plane with its centre at origin '$O$'. There is non-uniform magnetic field $\overrightarrow{B}=\frac{B_{0}x}{2R}\widehat{k}$ (here $B_0$ is $+ve$ constant) is existing in the region. The magnetic force acting on semi circular wire will be along