Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii R 1 and R 2

Question

Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii R 1 ​ and R 2 ​ , Respectively. The ratio of masses of X and Y is

TestHub · Accepted Answer

As we know, 2 1 ​ m v 2 = q V or v = m 2 q V ​ ​ Centripetal force R m v 2 ​ = q × B × v ∴ v = m qBR ​ Hence, m 2 q V ​ ​ = m qBR ​ or R = ( q 2 mV ​ ) 1/2 × B 1 ​ Here, V , q and B are constants. ∴ R ∝ m And, m 2 ​ m 1 ​ ​ = ( R 2 ​ R 1 ​ ​ ) 2

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