Motion in a Magnetic Field

A particle having charge of $1 \mathrm{C}$, mass $1 \mathrm{kg}$ and speed $1 \mathrm{m} {\mathrm{s}}^{-1}$ enters a uniform magnetic field, having magnetic induction of $1 \mathrm{T}$, at an angle $\mathrm{\theta }=\mathrm{30}°$  between velocity vector and magnetic induction. The pitch of its helical path is (in meters)

An electron gun G emits electron of energy $2 \mathrm{keV}$ travelling in the (+)ve x-direction. The electrons are required to hit the spot S where $GS=0.1 \mathrm{m}$ & the line GS makes an angle of ${\mathrm{60}}^{\mathrm{o}}$ with the x-axis, as shown in the fig. A uniform magnetic field $\overrightarrow{B}$ parallel to GS exists in the region outsides to electron gun. Find the minimum value of B needed to make the electron hit S.

A proton of mass $m$ and charge $+e$ is moving in a circular orbit in a magnetic field with energy $1 \mathrm{MeV}$. What should be the energy of $\mathrm{\alpha }-\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}$ ($\mathrm{mass}=4 \mathrm{m}$ and $\mathrm{charge}=+2e$), so that it can revolve in the path of same radius.

In the cyclotron, as radius of the circular path of the charged particle increases ($\omega =$ angular velocity, $v=$ linear velocity)

In the cyclotron, as radius of the circular path of the charged particle increases ($\omega =$ angular velocity, $v=$ linear velocity)

A particle of charge $e$ and mass $m$ moves with a velocity $v$ in a magnetic field $B$ applied perpendicular to the motion of the particle. The radius $r$ of its path in the field is

A proton, a deuteron and an $\alpha$-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $r_p, r_d$ and $r_{\alpha }$ denote, respectively, the radii of the trajectories of these particles, then

A proton of mass $m$ and charge $+e$ is moving in a circular orbit in a magnetic field with energy $1 \mathrm{MeV}$. What should be the energy of $\mathrm{\alpha }-\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}$ ($\mathrm{mass}=4 \mathrm{m}$ and $\mathrm{charge}=+2e$), so that it can revolve in the path of same radius.

A particle of charge $q$ and mass$m$, moving with a velocity $v$ along the $x$ -axis, enters the region $\left(x>0\right)$ with uniform magnetic field$B$ along the $\hat{\mathrm{k}}$ direction. The particle will penetrate in this region in the $x$ -direction up to a distance $d$ equal to

If a very high magnetic field is applied to a stationary charge then, the charge experiences no force.

A charge enters a uniform magnetic field at an angle $(0<\theta <{90}^{\circ })$. What will be the path of the charge? Also find its pitch?

A charged particle with the charge to mass ratio $\left(\frac{q}{m}\right)=\left(\frac{{10}^3}{19}\right) \mathrm{C} {\mathrm{kg}}^{-1}$ enters in a uniform magnetic field $\overrightarrow{\mathrm{B}}=(20\hat{\mathrm{i}}-30\hat{\mathrm{j}}+50\hat{\mathrm{k}}) \mathrm{T}$ at time $t=0$ with velocity $\overrightarrow{v}=(20\hat{\mathrm{i}}+50\hat{\mathrm{j}}+30\hat{\mathrm{k}}) \mathrm{m} {\mathrm{s}}^{-1}$. Assume that magnetic field exists in large space. The pitch of the helical path of the motion of the particle is $\frac{\pi }{n}$(in meter). Write the value of $n$.

Uniform electric and magnetic fields with strength $E$ and induction $B$, respectively, are along $y-$axis as shown in figure. A particle with specific charge $q/m$ leaves the origin $O$ in the direction of $x-$axis with an initial non-relativistic velocity $v_0$. The coordinate $y_n$ of the particle when it crosses the $y-$axis for the $n^{th}$ time is

Discuss the motion of a charged particle the uniform magnetic field considering some angle between the magnetic field and velocity of the particle.

The kinetic energy of the emergent proton beam $(\mathrm{in} \mathrm{MeV})$ from a cyclotron oscillator having frequency of $12\mathrm{ }\mathrm{M}\mathrm{H}\mathrm{z}$ and dee radius $60 \mathrm{cm}$?$\left(\mathrm{q}=1.6\times {10}^{-19}\mathrm{ }\mathrm{C},\mathrm{ }{\mathrm{m}}_{\mathrm{p}}=1.67\times {10}^{-27}\mathrm{k}\mathrm{g}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }1\mathrm{ }\mathrm{M}\mathrm{e}\mathrm{V}=1.6\times {10}^{-13}\mathrm{J}\mathrm{ }\right)$

A proton, a deuteron and an $\mathrm{\alpha }$ -particle with same kinetic energy enter perpendicularly in a uniform magnetic field. Then, the ratio of radii of their circular path is:

An electron of energy $1800\mathrm{ }\mathrm{e}\mathrm{V}\mathrm{ }$describes a circular path in the magnetic field of flux density $0.4\mathrm{ }\mathrm{T}$. The radius of the path is: $\left(q=1.6\times {10}^{-19}\mathrm{ }\mathrm{C},\mathrm{ }{m}_{\mathrm{e}}=9.1\times {10}^{-31}\mathrm{ }\mathrm{k}\mathrm{g}\right)$

The mass of a proton is 1847 times that of an electron. A electron and a proton are injected into a uniform electric field at right angle to the direction of the field with the same initial K.E.

In a crossed field, the magnetic field induction is 2.0T and electric field intensity is $20\times {10}^{3}V/m$ . At which velocity the electron will travel in a straight line without the effect of electric and magnetic fields?

An electron enters a region where magnetic field [B] and electric field [E] are mutually perpendicular, then