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Magnetic Fields due to Electric Current — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsMagnetic Fields due to Electric Current1 Mark
MCQ
Two particles $X$ and $Y$ having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii $r_1$ and $r_2$ respectively. The ratio of the mass of $X$ to that of $Y$ is
  • A
    $\frac{r_1}{r_2}$
  • B
    $\sqrt{\frac{r_1}{r_2}}$
  • C
    $\left[\frac{r_2}{r_1}\right]^2$
  • ✓
    $\left[\frac{r_1}{r_2}\right]^2$
✓

Answer

Correct option: D.
$\left[\frac{r_1}{r_2}\right]^2$
(d) : Radius of circular path described by a particle of charge $q$ and mass $m$ after being accelerated through a potential difference $V$ is
$
R=\frac{1}{B} \sqrt{\frac{2 V m}{q}}
$
Since, $B, V$ and $q$ are same for both the particles,
$
\therefore \quad \frac{r_1}{r_2}=\sqrt{\frac{m_x}{m_y}} \text { or } \frac{m_x}{m_y}=\left(\frac{r_1}{r_2}\right)^2
$

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