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Assertion If a charged particle is prone...

Assertion If a charged particle is pronected in a region, where `B` is perpendicular to velocity of projection, then the net force acting on the particle is independent orf its mass.
Reason The particle is performing uniform circular motion and force acting on it is `(mv^(2))/(r)`.

A

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

B

(b)If both Assertion and Reason are true but Reason is not correct explanation of Assertion.

C

(c)If Assertion is true but Reason is false.

D

(d)If Assertion is false but Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we will analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that if a charged particle is projected in a region where the magnetic field (B) is perpendicular to the velocity (v) of the particle, then the net force acting on the particle is independent of its mass. - **Explanation**: When a charged particle moves in a magnetic field, it experiences a magnetic force given by the Lorentz force law: \[ F = q(\mathbf{v} \times \mathbf{B}) \] Here, \(q\) is the charge of the particle, \(\mathbf{v}\) is the velocity vector, and \(\mathbf{B}\) is the magnetic field vector. The direction of the force is perpendicular to both the velocity and the magnetic field. 2. **Understanding the Reason**: The reason states that the particle is performing uniform circular motion and the force acting on it is given by: \[ F = \frac{mv^2}{r} \] where \(m\) is the mass of the particle, \(v\) is its speed, and \(r\) is the radius of the circular path. - **Explanation**: In uniform circular motion, the net force acting on the particle is indeed given by the centripetal force formula \(F = \frac{mv^2}{r}\). However, this force is not the magnetic force itself but rather the centripetal force required to keep the particle moving in a circular path. 3. **Analyzing the Relationship**: - The assertion claims that the net force is independent of mass, which is true because the magnetic force depends only on charge and velocity. - The reason, however, is not entirely correct in the context of the assertion. While the particle does undergo uniform circular motion due to the magnetic force, the expression \(F = \frac{mv^2}{r}\) does not imply that the magnetic force is independent of mass. 4. **Conclusion**: - The assertion is true: the magnetic force on the charged particle is independent of its mass. - The reason is not correct in the context of the assertion since it misrepresents the relationship between the forces involved. ### Final Answer: The correct answer is: **Assertion is true, but Reason is not correct.**
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