A proton and a deuteron (q=+e, m=2.0 u) havi | vedclass

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

Question

(C) In a uniform magnetic field,the radius $R$ of the circular path of a charged particle is given by:$R = \frac{mv}{qB} = \frac{\sqrt{2m(K.E.)}}{qB}$

Vedclass · Accepted Answer

$\sqrt{2}: 1$

Vedclass · Answer

(C) In a uniform magnetic field,the radius $R$ of the circular path of a charged particle is given by:$R = \frac{mv}{qB} = \frac{\sqrt{2m(K.E.)}}{qB}$Since both particles have the same kinetic energy $(K.E.)$ and move in the same magnetic field $(B)$,we have:$R \propto \frac{\sqrt{m}}{q}$For a proton,$m_p = m$ and $q_p = e$. For a deuteron,$m_d = 2m$ and $q_d = e$.The ratio of the radii is:$\frac{r_d}{r_p} = \frac{\sqrt{m_d}/q_d}{\sqrt{m_p}/q_p} = \sqrt{\frac{m_d}{m_p}} 	imes \frac{q_p}{q_d}$Substituting the values:$\frac{r_d}{r_p} = \sqrt{\frac{2m}{m}} 	imes \frac{e}{e} = \sqrt{2} 	imes 1 = \sqrt{2}$Therefore,the ratio $r_d : r_p$ is $\sqrt{2} : 1$.

$A$ proton and a deuteron $(q=+e, m=2.0 \ u)$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$,moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of the deuteron path to the radius $r_p$ of the proton path is:

Similar Questions

If a proton enters perpendicularly into a magnetic field with velocity $v$,the time period of revolution is $T$. If the proton enters with velocity $2v$,what will be the time period?

An alpha particle moving with a certain speed towards the east enters a uniform magnetic field directed vertically up. The alpha particle will then move in:

$A$ charged particle is moving along a magnetic field line. What is the magnetic force acting on the particle? $(\sin 0^{\circ}=0, \sin \frac{\pi}{2}=1)$

An electron is travelling in the east direction and a magnetic field is applied in the upward direction. In which direction will the electron deflect?

Work done by a magnetic field of $1\,T$ on a particle of charge $1\,C$ moving with a speed of $5\,m/s$ in one second is........$J$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module