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Question
(a) An electron moves along a circle of radius 1 m in a perpendicular magnetic field of strength 0.50 T. What would be its speed? Is it reasonable? (b) If a proton moves along a circle of the same radius in the same magnetic field, what would be its speed?
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Solution
Given:
(a) Radius of the circle = 1 m
Magnetic field strength = 0.50 T
We know:
`r = (m_ev_e)/(Be)`
`ve = (rBe)/(BE) , "where m_e is mass of the electron of the speed of the electron"`
`= (1 xx0.50xx1.6xx10^-19)/(9.1xx10^10 m/s)`
≈ 8.8 × 1010 m/s
Since, the speed of the electron moving along the circle is greater than the speed of light, it is not reasonable.
(b) For a proton,
`r = (m_pv_p)/(Be)`
`v_p = (rBe)/(m_p)`
where mp is the mass of the proton and vp is its speed.
`r = (1xx0.50xx1.6xx10^-19)/(1.6xx10^-27)`
r = 5 × 107 m/s
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