Lorentz Force

A charge particle of $2 \mathrm{\mu C}$ accelerated by a potential difference of $100 \mathrm{V}$ enters a region of uniform magnetic field of magnitude $4 \mathrm{mT}$ at right angle to the direction of field. The charge particle completes semicircle of radius $3 \mathrm{cm}$ inside magnetic field. The mass of the charge particle is ______ $\times {10}^{-18} \mathrm{kg}$.

A velocity selector consists of electric field $\overrightarrow{E}=E \hat{\mathrm{k}}$ and magnetic field $\overrightarrow{B}=B \hat{\mathrm{j}}$ with $B=12 \mathrm{mT}$. The value $E$ required for an electron of energy $728\mathrm{eV}$ moving along the positive $\mathrm{x}$-axis to pass undeflected is 

(Given, mass of electron $=9.1\times {10}^{-31} \mathrm{kg}$)

A charge particle is moving in a uniform magnetic field $\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}\right) \mathrm{T}$. If it has an acceleration of $\left(\mathrm{\alpha }\hat{\mathrm{i}}-4\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-2}$, then the value of $\alpha$ will be

An electron with energy $0.1 \mathrm{keV}$ moves at right angle to the earth's magnetic field of $1\times {10}^{-4} \mathrm{Wb} {\mathrm{m}}^{-2}$. The frequency of revolution of the electron will be
(Take mass of electron $=9.0\times {10}^{-31} \mathrm{kg}$)

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $6:5$ and their respective masses ratio is $9:4$. Then, the ratio of their charges will be

Given below are two statements :
Statement $\mathrm{I}$: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.
Statement $\mathrm{II}$: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.

Reason (R): Moving charged particle experiences magnetic force perpendicular to its direction of motion.

A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to $4$ times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle?

A singly ionized magnesium ion$\left(A=24\right)$  is accelerated to kinetic energy $5\mathrm{keV}$, and is projected perpendicularly into a magnetic field $B$ of the magnitude $0.5 \mathrm{T}$. The radius of path formed will be _____ $\mathrm{cm}.$

A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angles to the field. If $r_d$ and $r_p$ are the radii of their circular paths respectively, then the ratio $\frac{r_d}{r_p}$ will be $\sqrt{x}:1$, where $x$ is _____ .

Two long parallel conductors $S_1$ and $S_2$ are separated by a distance $10 \mathrm{cm}$ and carrying currents of $4 \mathrm{A}$ and $2 \mathrm{A}$ 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 $\overrightarrow{v}=\left(2\hat{i}+3\hat{j}\right) \mathrm{m} {\mathrm{s}}^{-1}$; where $\hat{i}$ & $\hat{j}$ represents unit vector along $x$ & $y$ axis respectively. The force acting on the charge particle is $4\pi \times {10}^{-5}\left(-x\hat{\mathrm{i}}+2\hat{\mathrm{j}}\right) \mathrm{N}$. The value of $x$ is 

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is 

The magnetic field vector of an electromagnetic wave is given by $B=B_0\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}\cos \left(kz-\omega t\right)$ where $\hat{\mathrm{i}}, \hat{\mathrm{j}}$ represents unit vector along $x$ and $y$-axis respectively. At $t=0 \mathrm{s},$ two electric charges $q_1$ of $4\pi$ coulomb and $q_2$ of $2\pi$ coulomb located at $\left(0, 0, \frac{\pi }{k}\right)$ and $\left(0, 0, \frac{3\pi }{k}\right),$ respectively, have the same velocity of $0.5\mathrm{c}\hat{\mathrm{i}},$ (where $c$ is the velocity of light ). The ratio of the force acting on charge $q_1$ to $q_2$ is :

Two ions of masses $4 \mathrm{amu}$  and $16 \mathrm{amu}$ have charges $+2 \mathrm{e}$ and $+3 \mathrm{e}$ respectively. These ions pass through the region of the constant perpendicular magnetic field. The kinetic energy of both ions is the same. Then:

A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let $r_{\mathrm{d}}$ and $r_{\mathrm{\alpha }}$ be their respective radii of circular path. The value of $\frac{r_{\mathrm{d}}}{r_{\mathrm{\alpha }}}$ is equal to:

Two ions having same mass have charges in the ratio $1: 2$. They are projected normally in a uniform magnetic field with their speeds in the ratio $2: 3$. The ratio of the radii of their circular trajectories is,

A charge $Q$ is moving $\mathrm{d}\overrightarrow{l}$ distance in the magnetic field $\overrightarrow{B}$. Find the value of work done by $\overrightarrow{B}$.

A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them ______ is and their speed is ______ in the ratio.

A particle of charge $q$ and mass $m$ is moving with a velocity $-v\hat{i}(v\ne 0)$ towards a large screen placed in the $Y-Z$ plane at distance d. If there is magnetic field $\overrightarrow{B}=B_0\hat{k},$ the minimum value of $v$ for which the particle will not hit the screen is :

A charged particle carrying charge $1 \mu C$ is moving with velocity $(2\hat{i}+3\hat{j}+4\hat{k}) \mathrm{m} {\mathrm{s}}^{-1}$. If an external magnetic field of $(5\hat{i}+3\hat{j}-6\hat{k})\times {10}^{-3}T$ exists in the region where the particle is moving then the force on the particle is $\overrightarrow{\mathrm{F}}\times {10}^{-9} \mathrm{N}$ . the vector $\overrightarrow{\mathrm{F}}$ is :