An electron enters the space between the plates of a charged capacitor as shown. The charge density on the plate is $\sigma $. Electric intensity in the space between the plates is $E$. A uniform magnetic field $B$ also exists in that space perpendicular to the direction of $E$. The electron moves perpendicular to both $\vec E$ and $\vec B$ without any change in direction. The time taken by the electron to travel a distance $\ell $ is the space is
Medium
Download our app for free and get started
Force on the electron due to the electric field $\mathrm{E}$ is
$\mathrm{F}_{\mathrm{E}}=(-\mathrm{e}) \mathrm{E}$
Force on the electron due to the magnetic field $B$ is
$\mathrm{F}_{\mathrm{B}}=(-\mathrm{e}) \mathrm{v} \mathrm{B}$
The electron will move in the fields undeflected, if these two forces are equal and opposite.
$\mathrm{eE}=\mathrm{evB} \quad$ or $\quad \mathrm{v}=\frac{\mathrm{E}}{\mathrm{B}}$
Electric field between the plates is $\mathrm{E}=\frac{\sigma}{\varepsilon_{0}}$
$\therefore \mathrm{v}=\frac{\sigma}{\varepsilon_{0} \mathrm{B}}$
The time taken by the electron to travel a distance $\ell$ in the space is $t=\frac{\ell}{V}=\frac{\ell}{\frac{\sigma}{\varepsilon_{0} B}}=\frac{\ell \varepsilon_{0} B}{\sigma}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A uniform magnetic field of $3000\,G$ is established in the positive $z-$ direction. A rectangular loop of side $10\,cm$ and $5\,cm$ carries a current of $12\,A.$ What is the magnitude of placed as shown torque on the loop isView Solution
- 2A square loop of side $a$ hangs from an insulating hanger of spring balance. The magnetic field of strength $B$ occurs only at the lower edge. It carries a current $I$. Find the change in the reading of the spring balance if the direction of current is reversedView Solution
- 3A charge particle of charge $q$ and mass $m$ is accelerated through a potential diff. $V\, volts$. It enters a region of orthogonal magnetic field $B$. Then radius of its circular path will beView Solution
- 4A moving coil galvanometer has resistance $50\,\Omega $ and it indicates full deflection at $4\,mA$ current. A voltmeter is made using this galvanometer and a $5\,k\Omega $ resistance. The maximum voltage, that can be measured using this voltamenter, will be close to ......$V$View Solution
- 5A tightly wound $100$ turns coil of radius $10 \mathrm{~cm}$ carries a current of $7 \mathrm{~A}$. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4 \pi \times 10^{-7} \mathrm{SI}$ units):View Solution
- 6Two straight long conductors $AOB$ and $COD$ are perpendicular to each other and carry currents ${i_1}$ and ${i_2}$. The magnitude of the magnetic induction at a point $ P$ at a distance a from the point $O$ in a direction perpendicular to the plane $ACBD$ isView Solution
- 7A milli voltmeter of $25\,millivolt$ range is to be converted in to an ammeter of $25\,A$ range. The value (in $ohm$) of necessary shunt will beView Solution
- 8The circular coil of a galvanometer has fifty turns. The coil has a radius of $1\ cm$. The coil is placed in a radial magnetic field of $0. 010\ T$. The torsion coefficent of the spring on which the coil hangs is $3 \times 10^{-7}\ N-m-rad^{-1}$. Determine the deviation of the galvanometer's hand if the current through the coil is $1.0\ mA$......$^o$View Solution
- 9View SolutionWhat are the directions of the magnetic field between and outside a pair of two parallel large sheets carrying currents in the same directions, as illustrated in Figure (from the side shown)?
- 10View SolutionField inside a solenoid is