Answer:
r = 0.001137 m = 1.137 mm
T = 3.57 x 10⁻¹⁰ s
Explanation:
In order for the electron to remain in a fixed circle centripetal force must be equal to the magnetic force:
[tex]Centripetal\ Force = Magnetic\ Force\\\frac{mv^2}{r} = qvB\ Sin\theta\\\\r = \frac{mv^2}{qvB\ Sin\theta} = \frac{mv}{qB\ Sin\theta}[/tex]
where,
r = radius = ?
m = mass of electron = 9.1 x 10⁻³¹ kg
v = speed of electron = 2 x 10⁷ m/s
q = charge on electron= 1.6 x 10⁻¹⁹ C
B = Magnetic Fild Strength = 0.1 T
θ = Angle between velocity and magnetic field = 90° (perpendicular)
[tex]r = \frac{(9.1\ x\ 10^{-31}\ kg)(2\ x\ 10^7\ m/s)}{(1.6\ x\ 10^{-19}\ C)(0.1\ T)Sin90^o}\\\\[/tex]
r = 0.001137 m = 1.137 mm
Now, for the period of the electron:
[tex]v = \frac{2\pi r}{T}\\\\T = \frac{2\pi r}{v}\\[/tex]
where,
T = Time period required o cover a distance equal to cirumference = ?
[tex]T = \frac{2\pi(0.001137\ m)}{2\ x\ 10^7\ m/s}\\\\[/tex]
T = 3.57 x 10⁻¹⁰ s
