Math Problem Statement
A charged particle moves without an initial velocity in a homogeneous electric field. After passing through a potential difference 𝑉 V, the particle enters a homogeneous magnetic field with induction 𝐵 B, perpendicular to the field lines. In the magnetic field, the particle moves in circular trajectories with a radius 𝑅 R. Determine the specific charge (the ratio of charge to mass) of the particle.
Solution
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Math Problem Analysis
Mathematical Concepts
Kinetic Energy
Lorentz Force
Circular Motion
Potential Difference
Magnetic Induction
Formulas
Kinetic Energy = eV
Kinetic Energy = 0.5mv^2
Lorentz Force = evB
Centripetal Force = mv^2/R
Specific Charge: e/m = 2V / (B^2R^2)
Theorems
Energy Conservation Principle
Newton's Second Law for Circular Motion
Suitable Grade Level
University Physics (Introductory Level)
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