Question

An electron of mass \( 9.0 \times 10^{-31} \) kg under the action of a magnetic field moves in a circle of radius 2 cm at a speed of \( 3 \times 10^6 \) m/s. A proton of mass \( 1.8 \times 10^{-27} \) kg moves in a circle of same radius in the same magnetic field, then its speed will become

• A. \( 1.5 \times 10^3 \, \text{m/s} \)
• B. \( 3 \times 10^6 \, \text{m/s} \)
• C. \( 6 \times 10^4 \, \text{m/s} \)
• D. \( 1.0 \times 10^5 \, \text{m/s} \)

Hint:

The velocity of a charged particle moving in a magnetic field is inversely proportional to its mass for a given radius and charge.

Answer 1

The Correct Option is C

Using the formula for the motion of charged particles in a magnetic field \( r = \frac{mv}{qB} \), we can equate the radius of the electron and proton's motion to find the proton's velocity. The speed of the proton turns out to be \( 6 \times 10^4 \, \text{m/s} \).