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Statement-1 Path of a charged particle i...

Statement-1 Path of a charged particle in a uniform and steady magnetic field cannot be parabolic
Statement-2 Magnetic field cannot accelerate a charged particle

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2, is True, Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both statements provided and determine their validity based on the principles of physics related to charged particles in a magnetic field. ### Step-by-Step Solution: **Step 1: Analyze Statement 1** - **Statement 1** claims that the path of a charged particle in a uniform and steady magnetic field cannot be parabolic. - In a uniform magnetic field, the force acting on a charged particle is given by the Lorentz force equation: \[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \] where \( q \) is the charge, \( \mathbf{v} \) is the velocity vector, and \( \mathbf{B} \) is the magnetic field vector. - The force is always perpendicular to the velocity of the charged particle. Therefore, the magnetic force does not do work on the particle and cannot change its speed, only its direction. **Conclusion for Step 1:** - Since the force is always perpendicular to the velocity, the path of the charged particle will be circular or helical, but not parabolic. Thus, **Statement 1 is true**. **Step 2: Analyze Statement 2** - **Statement 2** states that the magnetic field cannot accelerate a charged particle. - While it is true that the magnetic force does not change the speed of the particle (as it is perpendicular to the velocity), it can still cause a change in direction, which is a form of acceleration. - The acceleration \( \mathbf{a} \) can be defined as: \[ \mathbf{a} = \frac{\mathbf{F}}{m} \] where \( m \) is the mass of the particle. Since there is a force acting on the particle, there is indeed an acceleration. **Conclusion for Step 2:** - Therefore, **Statement 2 is false** because the magnetic field can change the direction of the particle, which constitutes acceleration. ### Final Conclusion: - **Statement 1 is true** and **Statement 2 is false**.
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