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

The assertion that a proton and an electron, entering a uniform magnetic field with identical momentum and perpendicular to the field, will trace circular paths of equal radius is true. This is because the magnetic force serves as the centripetal force for circular motion.
The reason provided is also true: The radius of the circular trajectory for a charged particle within a magnetic field is determined by the formula \( r = \frac{p}{qB} \), where \( p \) represents momentum, \( q \) denotes charge, and \( B \) indicates magnetic field strength.
Given that both the proton and the electron share the same momentum and are subjected to the same magnetic field, their paths will exhibit the same radius.
Consequently, both the assertion and the reason are accurate, and the reason logically substantiates the assertion.