Chapter 27: Problem 2
A particle of mass 0.195 g carries a charge of -2.50 \(\times\) 10\(^{-8}\) C. The particle is given an initial horizontal velocity that is due north and has magnitude 4.00 \(\times\) 10\(^4\) m/s. What are the magnitude and direction of the minimum magnetic field that will keep the particle moving in the earth's gravitational field in the same horizontal, northward direction?
Short Answer
Step by step solution
Understand the Forces
Express the Gravitational Force
Determine the Necessary Magnetic Force
Use the Lorentz Force Equation
Solve for the Magnetic Field Magnitude
Determine the Direction of the Magnetic Field
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Lorentz Force
- \( F_m = qvB\sin\theta \)
Gravitational Force
- \( F_g = mg \)
Magnetic Field Direction
- Point your fingers in the direction of the particle's velocity (northward).
- Align your palm to "push" in the direction of the force required to balance gravity (upwards).
- Your thumb, extending perpendicular to both, indicates the magnetic field direction (west).
Charged Particle Motion
- The velocity vector points north.
- The magnetic force, exerting force perpendicular to its direction, keeps the particle moving in the plane by offsetting other forces, such as gravity.
- This keeps the particle in "circular" motion.