Question

An electron and a proton enter a region of uniform magnetic field in a direction perpendicular to the field with the same kinetic energy. They revolve in circular paths of radii $r_e$ and $r_p$ respectively. Then

• A. $r_e=r_p$
• B. $r_e<r_p$
• C. $r_e>r_p$
• D. $r_e$ may be less or greater than $r_p$

Answer 1

The correct option is B $r_e<r_p$

Radius of the circular path, $r=\frac{mv}{qB}.......\left(1\right)$

$\because K.E=\frac{p^2}{2m}[\because p=mv]$

$\Rightarrow p=\sqrt{2m(K.E)}$

$\left(1\right)$ becomes,

$r=\frac{\sqrt{2m(K.E)}}{qB}$

Here, $B$ and $K.E.$ are same.

$\therefore r\propto \frac{\sqrt{m}}{q}.......\left(2\right)$

From $\left(2\right)$ we can write,

$\Rightarrow \frac{r_e}{r_p}=\sqrt{\frac{m_e}{m_p}}\left(\frac{q_p}{q_e}\right)[\because q_e=q_p]$

$\Rightarrow \frac{r_e}{r_p}=\sqrt{\frac{m_e}{m_p}}[\because m_e<m_p]$

$\therefore r_e<r_p$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, option (b) is the correct answer.

Why this question ? Understanding, how different physical quantities will vary (or) change as the motion of a charged particle is affected by magnetic field.