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Assertion : Path of a charged particle i...

Assertion : Path of a charged particle in uniform magnetic field cannot be a parabola.
Reason : For parabolic path acceleration should be constant.

A

If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.

B

If both Assertion and Reason are true but Reason is not the correct explanation of Assertion

C

If Assertion is true, but the Reason is false.

D

If Assertion is false but the Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the given assertion and reason, we will break down the concepts involved step by step. ### Step 1: Understanding the Assertion The assertion states that the path of a charged particle in a uniform magnetic field cannot be a parabola. **Explanation**: In a uniform magnetic field, the magnetic force acting on a charged particle is always perpendicular to its velocity. This perpendicular force does not do work on the particle (since work is force times displacement in the direction of the force), meaning that the speed of the particle remains constant. The only paths that can be maintained under such conditions are circular or helical paths, not parabolic. ### Step 2: Understanding the Reason The reason states that for a parabolic path, the acceleration should be constant. **Explanation**: In kinematics, a parabolic trajectory (like that of a projectile) typically occurs under constant acceleration (like gravity). However, the assertion is about the behavior of a charged particle in a magnetic field, where the acceleration is not constant due to the nature of the magnetic force being always perpendicular to the velocity. Thus, while it is true that a parabolic path requires constant acceleration, this does not apply to the scenario of a charged particle in a magnetic field. ### Step 3: Conclusion Based on the above analysis: - The assertion is **correct**: A charged particle in a uniform magnetic field cannot follow a parabolic path. - The reason is **incorrect**: While a parabolic path typically involves constant acceleration, the assertion does not depend on this condition. ### Final Answer The correct option is (C): Assertion is correct, but Reason is incorrect. ---

To analyze the given assertion and reason, we will break down the concepts involved step by step. ### Step 1: Understanding the Assertion The assertion states that the path of a charged particle in a uniform magnetic field cannot be a parabola. **Explanation**: In a uniform magnetic field, the magnetic force acting on a charged particle is always perpendicular to its velocity. This perpendicular force does not do work on the particle (since work is force times displacement in the direction of the force), meaning that the speed of the particle remains constant. The only paths that can be maintained under such conditions are circular or helical paths, not parabolic. ...
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