Question

Assertion (A): An electron and a proton enter with the same momentum \( \vec{p} \) in a magnetic field \( \vec{B} \) such that \( \vec{p} \perp \vec{B} \). Then both describe a circular path of the same radius.
Reason (R): The radius of the circular path described by the charged particle (charge \( q \), mass \( m \)) moving in the magnetic field \( \vec{B} \) is given by \( r = \frac{mv}{qB} \).

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false and Reason (R) is also false.

Hint:

For a charged particle in a magnetic field, the radius of the circular motion depends on its momentum, charge, and magnetic field strength.

Answer 1

The Correct Option is A

The assertion is correct because when an electron and a proton enter the magnetic field with the same momentum, they experience the same force due to their charge and follow a circular path with the same radius. The radius of the circular path is given by the formula: \[ r = \frac{p}{qB} \] Since both have the same momentum and the formula depends on \( p \), the radii of their circular paths will be the same. Thus, both the assertion and the reason are true, and the reason correctly explains the assertion.