Two particles of charges +Q and -Q are projec | vedclass

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

Question

(D) The time period of a charged particle in a magnetic field is given by $T = \frac{2\pi m}{QB}$.For the first particle with mass $M$ and charge $Q$,

Vedclass · Accepted Answer

$4\pi Mv \cos	heta / QB$

Vedclass · Answer

(D) The time period of a charged particle in a magnetic field is given by $T = \frac{2\pi m}{QB}$.For the first particle with mass $M$ and charge $Q$,the time period is $T_1 = \frac{2\pi M}{QB}$.For the second particle with mass $2M$ and charge $Q$,the time period is $T_2 = \frac{2\pi(2M)}{QB} = \frac{4\pi M}{QB}$.The particles will meet again when the time elapsed is a common multiple of their time periods. The least common multiple of $T_1$ and $T_2$ is $T = 4\pi M / QB$.At this time,the first particle completes $n_1 = T/T_1 = 2$ revolutions,and the second particle completes $n_2 = T/T_2 = 1$ revolution.The distance traveled along the direction of the magnetic field is given by $d = v \cos	heta 	imes t$.Substituting $t = T = \frac{4\pi M}{QB}$,we get $d = v \cos	heta 	imes \frac{4\pi M}{QB} = \frac{4\pi Mv \cos	heta}{QB}$.

Similar Questions

$A$ stream of electrons and protons are directed towards a narrow slit in a screen (see figure). The intervening region has a uniform electric field $E$ (vertically downwards) and a uniform magnetic field $B$ (out of the plane of the figure) as shown. Then:

$A$ particle of mass $m$ and charge $q$ moving with velocity $\vec v$ enters a region of uniform magnetic field $\vec B.$ Then:

$A$ proton of velocity $v = (3 \hat{i} + 2 \hat{j}) \ m/s$ enters a magnetic field of induction $B = (2 \hat{j} + 3 \hat{k}) \ T$. The acceleration produced in the proton in $m/s^2$ is (Specific charge of proton $= 0.96 \times 10^8 \ C/kg$)

In the figure shown,a charge $q$ of mass $m$ moving with a velocity $v$ along the $x$-axis enters a region of uniform magnetic field $B$ directed into the page. If the particle is able to enter the region $x > b$,then the velocity $v$ must be greater than:

Vedclass Test Series

Exam Paper Generator

Online Exam Module