Lorentz Transformation Equations

An electron moves in a circular orbit with a uniform speed $\mathrm{v}$. It produces a magnetic field $\mathrm{B}$ at the centre of the circle. The radius of the circle is proportional to 

A charge particle with charge $\mathrm{q}$ enters a region of constant uniform and mutually orthogonal field $\overrightarrow{\mathrm{E}}$ and $\overrightarrow{\mathrm{B}}$ with a velocity $\overrightarrow{\mathrm{v}}{\perp }^{\mathrm{r}}$ to both $\overrightarrow{\mathrm{E}}$ and $\overrightarrow{\mathrm{B}}$ and corner out without and change in magnitude or direction of $\overrightarrow{\mathrm{v}}$. Then

The magnetic field in a certain region is given by $\overrightarrow{\mathrm{B}}=8.35\times {10}^{-2} \hat{\mathrm{i}}\mathrm{T}$. A proton is shot into the field with velocity $\overrightarrow{\mathrm{v}}=\left(2\times {10}^5\hat{\mathrm{i}}+4\times {10}^5\hat{\mathrm{j}}\right) \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$. The proton follows a helical path in the field. The distance moved by proton in the $\mathrm{x}-$direction during the period of one revolution in the $\mathrm{y}-\mathrm{z}$ plane will be- $\left({\mathrm{m}}_{\mathrm{p}}=1.67\times {10}^{27}\mathrm{kg}\right)$.

The magnetic force acting on a charged particle of charge $-2\mathrm{\mu C}$ in a magnetic field of $2\mathrm{T}$ acting in $\mathrm{y}-$direction.When the particle velocity is $\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}\right)\times {10}^6 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$

The radius of our galaxy is about $3\times {10}^{20}\mathrm{m}$ with what speed should a person travel so that he can reach from the centre of the galaxy to its edge in $20$ years of his lifetime.

A rod of length $1 \mathrm{m}$ moves with a speed of $0.5 \mathrm{C}$. How much length contraction takes place $\%$.

A particle with a lifetime of $2\times {10}^{-6} \sec$ moves through the lab with a speed of $0.9 \mathrm{C}$. It's lifetime, as measured by an observer in the lab is 

A cube with sides of proper length ${\mathrm{l}}_0$ is viewed from a reference frame moving with velocity $\mathrm{V}$, parallel to an edge of the cube. The expression for the volume of the cube for the observer is 

An electric bulb, connected to a make and break power supply, switches off and on every second in its rest frame. What is the frequency of its switching off and on as seen from a spaceship travelling at a speed $0\cdot 8 \mathrm{c}$? (where $\mathrm{c}$ is speed of light).

A proton at rest is accelerated through a high potential difference. Speed acquired by proton is $2.5\times {10}^8 \mathrm{m}/\mathrm{s}$. Rest mass of proton is $1.67\times {10}^{-27} \mathrm{kg}$. The accelerating potential difference is $7\times {10}^x$. Find $x$.

A person travels by a car at a speed of $180 \mathrm{km}/\mathrm{h}$. It takes exactly $10 \mathrm{hours}$ by his wristwatch to go from the station A to the station B. What is the difference between rest distance and apparent distance covered between the two stations ?

An aeroplane travels over a rectangular field $100 \mathrm{m}\times 50 \mathrm{m}$, parallel to its length. What should be the speed of the plane so that the field becomes square in the plane frame ?