Two charged particles of specific charges in | vedclass

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

Question

(C) The radius $r$ of a circular path of a charged particle in a magnetic field is given by $r = \frac{mv}{qB}$.Since kinetic energy $K = \frac{1}{2}m

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) The radius $r$ of a circular path of a charged particle in a magnetic field is given by $r = \frac{mv}{qB}$.Since kinetic energy $K = \frac{1}{2}mv^2$,we have $mv = \sqrt{2mK}$.Substituting this into the radius formula,we get $r = \frac{\sqrt{2mK}}{qB} = \frac{1}{B} \sqrt{\frac{2K}{q^2/m}}$.Since specific charge $\alpha = \frac{q}{m}$,we can write $r = \frac{1}{B} \sqrt{\frac{2K}{m \alpha^2}}$.Given the ratio of specific charges $\frac{\alpha_1}{\alpha_2} = \frac{2}{1}$ and masses $\frac{m_1}{m_2} = \frac{1}{4}$.Since kinetic energy $K$ and magnetic field $B$ are the same for both,the ratio of radii is $\frac{r_1}{r_2} = \sqrt{\frac{m_1}{m_2}} \cdot \frac{\alpha_2}{\alpha_1}$.Substituting the values: $\frac{r_1}{r_2} = \sqrt{\frac{1}{4}} \cdot \frac{1}{2} = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}$.Thus,the ratio of the radii is $1:4$.

Similar Questions

An $\alpha$-particle and a proton travel with the same velocity in a magnetic field perpendicular to the direction of their velocities. Find the ratio of the radii of their circular paths.

An electron enters a region where the electrostatic field is $20\,N/C$ and the magnetic field is $5\,T$. If the electron passes undeflected through the region,then the velocity of the electron will be.....$m\,s^{-1}$.

$A$ proton moving with a constant velocity passes through a region of space without any change in its velocity. If $E$ and $B$ represent the electric and magnetic fields respectively,this region may have:

$A$ proton, a deuteron, and an $\alpha$-particle enter a region of a uniform magnetic field perpendicular to their velocities with the same kinetic energy. If $r_p, r_d,$ and $r_\alpha$ are the radii of the circular paths of these particles, respectively, then:

An electron is projected along the axis of a circular conductor carrying current $I$. The electron will experience:

Vedclass Test Series

Exam Paper Generator

Online Exam Module