An electron enters with a velocity {rm{vec v}},{{rm{v}}_0}{rm{hat{i}}} into a cubical region (faces

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4.Moving Charges and Magnetism

medium

An electron enters with a velocity ${\rm{\vec v}},{{\rm{v}}_0}{\rm{\hat i}}$ into a cubical region (faces parallel to coordinate planes) in which there are uniform electric and magnetic fields. The orbit of the electron is found to spiral down inside the cube in plane parallel to the $\mathrm{xy}$ - plane. Suggest a configuration of fields $\mathrm{E}$ and $\mathrm{B}$ that can lead to it.

Option A

Option B

Option C

Option D

Solution

Due to magnetic field, electron is moving on circular path in $x y$-plane linear speed of electron is increase by increasing electric field in $x$-direction, so that radius of trajectory of path also increases.

Thus, electron is moving on helical path.

Change magnetic field as, $\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{k}$

Now velocity of electron, $\vec{v}=v_{0} \hat{i}$

Magnetic force on electron when it enter in magnetic field,

$\overrightarrow{\mathrm{F}}=-e\left(v_{0} \hat{i} \times \mathrm{B}_{0} \hat{k}\right)$

$=-e v_{0} \mathrm{~B}_{0}(\hat{i} \times \hat{k})$

$=-e v_{0} \mathrm{~B}_{0}(-\hat{j})$

Standard 12

Physics

A proton (mass $ = 1.67 \times {10^{ – 27}}\,kg$ and charge $ = 1.6 \times {10^{ – 19}}\,C)$ enters perpendicular to a magnetic field of intensity $2$ $weber/{m^2}$ with a velocity $3.4 \times {10^7}\,m/\sec $. The acceleration of the proton should be

medium

An electron enters a chamber in which a uniform magnetic field is present as shown below. An electric field of appropriate magnitude is also applied, so that the electron travels undeviated without any change in its speed through the chamber. We are ignoring gravity. Then, the direction of the electric field is

medium

(KVPY-2013)

Ratio of electric and magnetic field due of moving point charge if its speed is $4.5 \times 10^{5} \;m / s$

hard

(AIIMS-2019)

A rectangular region of dimensions ( $\omega \times l(\omega) \ll l$ ) has a constant magnetic field into the plane of the paper as shown in the figure below. On one side, the region is bounded by a screen. On the other side, positive ions of mass $m$ and charge $q$ are accelerated from rest and towards the screen by a parallel plate capacitor at constant potential difference $V < 0$ and come out through a small hole in the upper plate. Which one of the following statements is correct regarding the charge on the ions that hit the screen?

normal

(KVPY-2017)

A proton of mass $1.67 \times {10^{ – 27}}\,kg$ and charge $1.6 \times {10^{ – 19}}\,C$ is projected with a speed of $2 \times {10^6}\,m/s$ at an angle of $60^\circ $ to the $X – $ axis. If a uniform magnetic field of $0.104$ $Tesla$ is applied along $Y – $ axis, the path of proton is

hard

(IIT-1995)

Solution

Similar Questions

A proton (mass $ = 1.67 \times {10^{ – 27}}\,kg$ and charge $ = 1.6 \times {10^{ – 19}}\,C)$ enters perpendicular to a magnetic field of intensity $2$ $weber/{m^2}$ with a velocity $3.4 \times {10^7}\,m/\sec $. The acceleration of the proton should be

Ratio of electric and magnetic field due of moving point charge if its speed is $4.5 \times 10^{5} \;m / s$

A proton of mass $1.67 \times {10^{ – 27}}\,kg$ and charge $1.6 \times {10^{ – 19}}\,C$ is projected with a speed of $2 \times {10^6}\,m/s$ at an angle of $60^\circ $ to the $X – $ axis. If a uniform magnetic field of $0.104$ $Tesla$ is applied along $Y – $ axis, the path of proton is

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