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 statement is accurate. When an electron and a proton enter a magnetic field with identical momentum, their experienced forces are equal due to their charges. This results in them traversing circular paths of the same radius. The radius of this circular path is determined by the equation: \[ r = \frac{p}{qB} \] Given that both particles possess the same momentum \( p \), and the radius formula is dependent on \( p \), their circular paths will consequently have the same radius. Therefore, both the assertion and the reason are valid, and the reason provides a correct explanation for the assertion.