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 R1 and R2 , respectively. The ratio of masses of X and Y is

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 R1 and R2 , respectively. The ratio of masses of X and Y is (A)  ((R1/R2))1/2  (B)  ((R2/R1))  (C)  ((R1/R2))2  (D)  ((R1/R2))

Tardigrade Admin · Accepted Answer

The radius of charged particle in magnetic field,

r = \frac{m v}{qB} = \frac{2 m E _{k}}{qB}

According to question, let

m_{x}

and

m_{y}

are the masses,

q

are charges and

B

magnetic field and

E_{K}

, kinetic energy. When the charged particles are accelerated at same potential, then

K E

will be same.
So, radius,

R_{1} = \frac{2 m _{x} \times E _{k}}{qB}

and

R_{2} = \frac{2 m _{y} E _{k}}{qB}

∴ \frac{m _{x}}{m _{y}} = (\frac{R _{1}}{R _{2}})^{2}

Q. 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

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

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

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

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

Q. 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 R1​ and R2​ , respectively. The ratio of masses of X and Y is

(R2​R1​​)1/2

(R1​R2​​)

(R2​R1​​)2

(R2​R1​​)

Q. 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

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

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

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

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