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Assertion If the path of a charged part...

Assertion If the path of a charged particle in a region of uniform electric and magnetic field is not a circle, then its kinetic energy may remain constant.
Reason In a combined electric and magnetic field region a moving charge experiences a net force
`F=qE+q(VxxB),` where symbols have their usual meanings.

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To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that if the path of a charged particle in a uniform electric and magnetic field is not circular, then its kinetic energy may remain constant. We need to evaluate whether this statement is true or false. 2. **Understanding the Reason**: The reason provided states that in a combined electric and magnetic field, a moving charge experiences a net force given by the equation \( F = qE + q(v \times B) \). This is known as the Lorentz force. 3. **Analyzing the Forces**: The Lorentz force consists of two components: - The electric force \( F_E = qE \) - The magnetic force \( F_B = q(v \times B) \) 4. **Effect of Electric Field**: The presence of an electric field \( E \) exerts a force on the charged particle that causes it to accelerate. This acceleration changes the velocity of the particle. 5. **Kinetic Energy Calculation**: The kinetic energy \( K \) of a charged particle is given by: \[ K = \frac{1}{2} mv^2 \] If the velocity \( v \) changes due to the electric field, the kinetic energy will also change. Therefore, if the path is not circular (for example, helical), the kinetic energy cannot remain constant. 6. **Conclusion on Assertion**: Since the electric field causes acceleration and thus a change in speed, the assertion that the kinetic energy may remain constant is incorrect. 7. **Conclusion on Reason**: The reason is correct as it accurately describes the net force acting on the charged particle in the presence of both electric and magnetic fields. 8. **Final Evaluation**: Therefore, we conclude that the assertion is false, while the reason is true. ### Final Answer: - Assertion: **False** - Reason: **True**
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