An electron moving in a uniform magnetic field $(4\hat{i}+6\hat{\mathit{j}}+n\hat{\mathit{k}}) \mathrm{T}$ experiences a force $(2\hat{i}+3\hat{j}+4\hat{k}) \mathrm{N}.$ Then the value of ${}^{\text{'}}\mathrm{n}^{\text{'}}$ is

An electron enters a magnetic field of $\left(3 \hat{i}+4 \hat{j}\right) \mathrm{T}$ with a velocity of $\left(6 \hat{j}+4 \hat{k}\right) \mathrm{m} {\mathrm{s}}^{-1}.$ The acceleration produced is

($\frac{e}{m}$ of electron $=1.76\times {10}^{11} \mathrm{C} {\mathrm{kg}}^{-1}$)

Two parallel metal plates $A$ and $B$ separated by a distance $25 \mathrm{cm}$ are connected to an ammeter. Photons of energy $3.28 \mathrm{eV}$ are incident on the photosensitive plate $A$ of threshold wavelength $5000 \stackrel{\mathrm{o}}{\mathrm{A}}$. The minimum value of the magnetic field to be applied parallel to the plates so that the current through the ammeter becomes zero is $\mathrm{B}\times {10}^{-5} \mathrm{T}$. Then the value of

$B$ is (mass of electron $=9.0\times {10}^{-31} \mathrm{kg}$, charge of electron $=1.6\times {10}^{-19}\mathrm{C}$ )

A disc of radius $R$ rotates with a constant angular velocity $\omega$ about its own axis. Surface charge density of this disc varies as $a=\alpha r^2$ where $\text{'}r\text{'}$ is the distance from center of the disc. The magnetic field intensity at the center of the disc is