Charged Particle Path

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A charge enters uniform B perpendicular to field. Path is?

RankGuru · Accepted Answer

1. **Force Logic**: The magnetic force $\vec{F} = q(\vec{v} 	imes \vec{B})$ is always perpendicular to the velocity.
2. **Energy Logic**: Since the force is perpendicular to displacement, work done is zero ($W = 0$). Kinetic energy and speed remain constant.
3. **Centripetal Motion**: A constant force acting perpendicular to the path of a constant speed object produces **uniform circular motion**.
4. **Radius**: $r = \frac{mv}{qB}$.
5. **Conclusion**: The trajectory in the plane perpendicular to the field is a **circle**.

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Charged Particle Path

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