Question

An electron in a television lamp moves in front of the tube at high speed

8. 10 ^ 6 m / s along the x-axis as shown. Magnetic fields create in

The tube is fitted with an angle of 60 ° to the x-axis

(in the xy plane) and

value 0. 025T.

a) Calculate the applied magnetic force and the acceleration of the electron.

b) Find rotation period, orbital radius and spiral step.

Answer 1

a) $F=|q|vB\sin\alpha=1.6\cdot10^{-19}\cdot8\cdot10^6\cdot0.025\cdot\sin60°=2.77\cdot10^{-14}\ (T)$

$a=F/m=2.77\cdot10^{-14}/9.1\cdot10^{-31}=3\cdot10^{16}\ (m/s^2)$

b) $qvB\sin60°=m(v\cdot\sin60)^2/r$ and $T=2\pi r/(v\cdot \sin60°)\to$ $T=\frac{2\pi m}{qB}=$

$=\frac{2\cdot3.14\cdot 9.1\cdot10^{-31}}{1.6\cdot10^{-19}\cdot0.025}=1.43\cdot10^{-9}\ (s)$

$r=\frac{vm}{qB}\cdot\sin60°=\frac{8\cdot 10^6\cdot 9.1\cdot10^{-31}}{1.6\cdot10^{-19}\cdot0.025}\cdot\sin60°=0.0016\ (m)$

$h=v\cdot\cos60°\cdot T=8\cdot10^6\cdot\cos60°\cdot1.43\cdot10^{-9}=0.00572\ (m)$