Two particles of equal charges after being accelerated through the same potential difference enter a uniform transverse magnetic field and describe circular path of radii R1 and R2 respectively. Then the ratio of their masses (M1/M2) is

Question

Two particles of equal charges after being accelerated through the same potential difference enter a uniform transverse magnetic field and describe circular path of radii R1 and R2 respectively. Then the ratio of their masses (M1/M2) is (A)  (R1/R2)  (B)  ( (R1/R2) )2  (C)  (R2/R1)  (D)  ( (R2/R1) )2

Tardigrade Admin · Accepted Answer

Radius of circular path R=(mv/qB) but mv=√2mqV ∴ R=(√2mqV/qB) Or R propto √m Or (R12/R22)=(M1/M2) Or (M1/M2)=(R12/R22)=( (R1/R2) )2

Q. Two particles of equal charges after being accelerated through the same potential difference enter a uniform transverse magnetic field and describe circular path of radii $R_{1}$ and $R_{2}$ respectively. Then the ratio of their masses $(M_{1} / M_{2})$ is

$\frac{R _{1}}{R _{2}}$

$(\frac{R _{1}}{R _{2}})^{2}$

$\frac{R _{2}}{R _{1}}$

$(\frac{R _{2}}{R _{1}})^{2}$

$(\frac{R _{1}}{R _{2}})^{1/2}$

Radius of circular path
$R = \frac{m v}{qB}$ but $m v = 2 m q V$
$∴$ $R = \frac{2 m q V}{qB}$
Or $R \propto m$
Or $\frac{R _{1}^{2}}{R _{2}^{2}} = \frac{M _{1}}{M _{2}}$
Or $\frac{M _{1}}{M _{2}} = \frac{R _{1}^{2}}{R _{2}^{2}} = (\frac{R _{1}}{R _{2}})^{2}$

Q. Two particles of equal charges after being accelerated through the same potential difference enter a uniform transverse magnetic field and describe circular path of radii R1​ and R2​ respectively. Then the ratio of their masses (M1​/M2​) is

R2​R1​​

(R2​R1​​)2

R1​R2​​

(R1​R2​​)2

(R2​R1​​)1/2

Radius of circular path R=qBmv​ but mv=2mqV​ ∴ R=qB2mqV​​ Or R∝m​ Or R22​R12​​=M2​M1​​ Or M2​M1​​=R22​R12​​=(R2​R1​​)2