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  • Two particles A and B, having equal charges, after being accelerated through the same potential difference enter a region of uniform magnetic field and the particles describe circular paths of radi

Two particles A and B, having equal charges, after being accelerated through the same potential difference enter a region of uniform magnetic field and the particles describe circular paths of radii R_1 and R_2 respectively. The ratio of the masses of A and B is

Option: 1

\sqrt{R_1 / R_2}


Option: 2

R_1 / R_2


Option: 3

\left(R_1 / R_2\right)^2


Option: 4

\left(R_2 / R_1\right)^2


Answers (1)

best_answer

For a circular path, magnetic force = centripetal force

i.e., q v B=\frac{m v^2}{R}

Again, \frac{1}{2} m v^2=q v

Hence, q v B=\frac{2 q v}{R}

or, R=\frac{2 V}{V B}=\frac{2 V}{B} \sqrt{\frac{m}{2 q V}}\left[\because V=\sqrt{\frac{2 q V}{m}}\right]

According to the question q, V and B are constants.

Therefore \frac{R_1}{R_2}=\sqrt{\frac{m_1}{m_2}} \text { or, } \frac{m_1}{m_2}=\left(\frac{R_1}{R_2}\right)^2

 

Posted by

shivangi.shekhar

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