A charged particle with a mass of 1 gram and a charge of +2 μC is released into a magnetic field of 0.5 T. Determine the radius of the circular path it follows if its initial velocity is 10 m/s perpendicular to the magnetic field.
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The equation for the radius of the circular path followed by a charged particle in a magnetic field is given by:
r = (mv)/(qB)
where r is the radius of the circular path, m is the mass of the charged particle, v is its velocity, q is its charge, and B is the magnetic field strength.
Given:
m = 1 gram = 0.001 kg
q = +2 μC = +2 × 10^(-6) C
v = 10 m/s
B = 0.5 T
Substituting these values into the equation:
r = (0.001 kg × 10 m/s) / ((+2 × 10^(-6) C) × 0.5 T)
Simplifying the equation:
r = (0.001 kg × 10 m/s) / (2 × 10^(-6) C × 0.5 T)
r = 0.001 kg × 10 m/s / 1 × 10^(-6) C × 0.5 T
r = (0.001 × 10 × 1) / (1 × 0.5)
r = 0.02 m
Therefore, the radius of the circular path followed by the charged particle is 0.02 meters.
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