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

$A$ charged particle moving in a magnetic field $B$ has velocity components both along $B$ and perpendicular to $B$. The path of the charged particle will be:

An electron is moving along the $+x$ direction. To make it move along an anticlockwise circular path in the $x-y$ plane,the magnetic field must be applied along:

The charged particle moving in a uniform magnetic field of $(3\hat{i} + 2\hat{j}) \ \text{T}$ has an acceleration $(4\hat{i} - \frac{x}{2}\hat{j}) \ \text{m/s}^2$. The value of $x$ is . . . . . . .

$A$ charge '$q$' moves with a velocity $2 \ m/s$ along the $x$-axis in a uniform magnetic field $\vec{B} = (2 \hat{i} + 2 \hat{j} + 3 \hat{k}) \ T$. The charge will experience a force:

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