Question

Assertion (A): A proton and an electron enter a uniform magnetic field \( \vec{B} \) with the same momentum \( \vec{p} \) such that \( \vec{p} \) is perpendicular to \( \vec{B} \). They describe circular paths of the same radius.
Reason (R): In a magnetic field, orbital radius \( r \) is equal to \( \frac{p}{qB} \).

• 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 charged particles moving in a magnetic field, the radius of the circular path is given by \( r = \frac{p}{qB} \), which depends on the momentum, charge, and magnetic field strength.

Answer 1

The Correct Option is A

Assertion (A) is true: Both a proton and an electron entering a uniform magnetic field with the same momentum and perpendicular to the magnetic field will follow circular paths of the same radius, as the magnetic force provides the centripetal force required for circular motion.
Reason (R) is true: The radius of the circular path for a charged particle in a magnetic field is given by \( r = \frac{p}{qB} \), where \( p \) is the momentum, \( q \) is the charge, and \( B \) is the magnetic field strength.
Since the momentum and magnetic field are the same for both the proton and the electron, they will describe circular paths of the same radius. Thus, both Assertion (A) and Reason (R) are true, and Reason (R) correctly explains Assertion (A).