What is the time period of an electron projected into a uniform magnetic field of 10 mT and moves in a circle of radius 6 cm? (Answer: 3.6 ns) 



Given:

Magnetic Field = B = 10 mT = 0.01 T

Radius = r = 6 cm = 0.06 m

[ ∴ Charge of Electron = q = 1.6 ｘ 10⁻¹⁹ C]
[ ∴ Mass of Electron = m = 9.11 ｘ 10⁻³¹ kg]



To Find:

The time period of Electron = T = ?


Solution:

The formula for the time period T of an electron moving in a circular trajectory is given:

T = `\frac {2ã„«m}{qB}`

by putting the corresponding values

T = `\frac {2 ｘ 3.1416 ｘ 9.11 ｘ 10⁻³¹ kg}{1.6 ｘ 10⁻¹⁹ C ｘ0.01 T}`

T = `\frac {5.72 ｘ 10⁻³⁰ kg}{1.6 ｘ 10⁻²¹ C T }`

T = 3.575 ï½˜ 10⁻³⁰⁺²¹ s

T = 3.575 ï½˜ ï½˜ 10⁻⁹ s

T = 3.6 ï½˜ 10⁻⁹ m s⁻¹ ------------------ Ans.



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