A beam of muons is maintained in a circular orbit by a uniform magnetic field. Neglect energy loss due to electromagnetic radiation and neglect any force that arises from variation in mass. The mass of the muon is 1.88 × 10–28 kg, its charge is –1.602 × 10–19C, and its half life is 1.523 µS. The speed of the muons is much less than the speed of light. It is found that half of the muons decay during each full orbit. The magnitude of magnetic field is found to be n(4.85 × 10

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Physics

Radioactivity New

Motion of Charged Particle in Uniform Magnetic Field

Question

A beam of muons is maintained in a circular orbit by a uniform magnetic field. Neglect energy loss due to electromagnetic radiation and neglect any force that arises from variation in mass. The mass of the muon is 1.88 × 10^–28 kg, its charge is –1.602 × 10^–19C, and its half life is 1.523 µS. The speed of the muons is much less than the speed of light. It is found that half of the muons decay during each full orbit. The magnitude of magnetic field is found to be n(4.85 × 10^–3) Tesla. Find the integer n ?]

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$T = \frac{2 πm}{qB} = T_{1 / 2}$
$B = \frac{2 πm}{q (T_{1 / 2})}$

⇒ B = 4.85 × 10^–3 T