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The radius of the circular path of a charged particle moving in a magnetic field is given by r = mv sin θ / Be. If r = 3 × 10⁵ sin 30° / 0.3 × 10⁸ = 3 × 10⁵ × 1 / 2 / 3 × 10⁷ = 0.5 × 10⁻² m = 0.5 cm, which of the following relationships is correct?
- The radius increases with an increase in velocity.
- The radius decreases as the magnetic field strength increases.
- The radius depends on the charge of the particle.
- The radius remains unaffected by changes in velocity.
Correct answer: The radius increases with an increase in velocity.
Solution
The formula for the radius of a charged particle in a magnetic field is r = mv / (qB). From this, it is evident that the radius is directly proportional to the velocity (v) of the particle, as all other terms are constants for a given situation.
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