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:

• A. \(\left(\dfrac{R_1}{R_2}\right)^{1/2}\)
• B. \(\left(\dfrac{R_2}{R_1}\right)^{1/2}\)
• C. \(\left(\dfrac{R_1}{R_2}\right)^2\)
• D. \(\left(\dfrac{R_2}{R_1}\right)^2\)

Hint:

In magnetic deflection: \[ r\propto\sqrt{m} \] if particles are accelerated through same potential.

Answer 1

The Correct Option is C

Step 1: Speed after acceleration: \[ v=\sqrt{\frac{2qV}{m}} \]
Step 2: Radius in magnetic field: \[ r=\frac{mv}{qB} \]
Step 3: Substituting: \[ r\propto\sqrt{m} \]
Step 4: Hence: \[ \frac{m_X}{m_Y}=\left(\frac{R_1}{R_2}\right)^2 \]