The figure shows a region of length l with a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The time period of a charged particle in a uniform magnetic field is given by $T = \frac{2 \pi m}{qB}$.The proton completes $10$ revolutions,so th

Vedclass · Accepted Answer

$0.44$

Vedclass · Answer

(C) The time period of a charged particle in a uniform magnetic field is given by $T = \frac{2 \pi m}{qB}$.The proton completes $10$ revolutions,so the total time spent in the magnetic field is $t = 10T = 10 	imes \frac{2 \pi m}{qB}$.The velocity component parallel to the magnetic field is $v_{\parallel} = v \cos(60^{\circ}) = v 	imes \frac{1}{2} = \frac{v}{2}$.Since the velocity component parallel to the magnetic field remains constant,the distance $l$ covered in the direction of the field is $l = v_{\parallel} 	imes t = \frac{v}{2} 	imes 10 	imes \frac{2 \pi m}{qB} = \frac{10 \pi m v}{qB}$.Substituting the given values:$l = \frac{10 	imes 3.14 	imes 1.67 	imes 10^{-27} 	imes 4 	imes 10^{5}}{1.6 	imes 10^{-19} 	imes 0.3}$$l = \frac{20.942 	imes 10^{-21}}{0.48 	imes 10^{-19}} = \frac{20.942}{48} \approx 0.436 \, m$.Rounding to the nearest option,$l \approx 0.44 \, m$.

Similar Questions

$A$ proton and a helium nucleus are shot into a magnetic field at right angles to the field with the same kinetic energy. The ratio of their radii is:

In a Bainbridge mass spectrograph,a potential difference of $1000 \ V$ is applied between two plates separated by a distance of $1 \ cm$. If the magnetic field is $B = 1 \ T$,what is the velocity of the undeflected positive ions in $m/s$ from the velocity selector?

An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57 \times 10^{-2} \, T$. If the value of $e/m$ is $1.76 \times 10^{11} \, C/kg$,the frequency of revolution of the electron is

$A$ charged particle is released from rest in a region of uniform electric and magnetic fields,which are parallel to each other. The locus of the particle will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module