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In a chamber, a uniform magnetic field o...

In a chamber, a uniform magnetic field of `6.5 G (1 G = 10^(-4) T)` is maintained. An electron is shot into field with a speed of `4.8 xx 10^(-6) ms^(-1)` normal to the field. Explain, why the path of the electron is a circle. Determine the radius of the circular orbit. `(e = 1.6 xx 10^(-19) C , m_e = 9.1 xx 10^(-31) kg)`.

Text Solution

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Here `B = 6.5 G = 6.5 xx 10^(-4) T, q = e = 1.6 xx 10^(-19) C, m_e = 9.1 xx 10^(-31) kg and v = 4.8 xx 10^(6) m s^(-1)`
When an electron is shot into the magnetic field in a direction normal to the field, force acting on it `[F = B e v]` is acting is a direction perpendicular to both `v` and B and provides the necessary centripetal force to make the path of electron a circular path.
Radius of the circular orbit, `r = (m_e v)/(e B) = (9.1 xx 10^(-31) xx 4.8 xx 10^(-6))/(1.6 xx 10^(-19) xx 6.5 xx 10^(-4)) = 4.2 xx 10^(-2) m " or " 4.2 cm`.
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