Magnetic Forces Question

Question

An electron is released from rest at point A. The electron then accelerates toward the negatively charged plate and leave the plate through a small hole at point B. The potential at point A is 2400 V greater than that of the point B.

1. Find the speed of the electron when it leaves the negatively charged plate.

2. If the particle enters a constant magnetic field of 100 Gauss and the speed is perpendicular to the field, find the magnitude of the radius of the circular trajectory.

Answer 1

1. eU = mv²/2; v = √2eU/m; e = 1.6·10^-19 C is charge of electron by value, m = 9.11·10^-31kg;

So, v = √2·1.6·10^-19·2400/(9,11·10^-31) = 2.9·10⁷ m/s

2 mv²/r = Bev; r = mv/Be; B = 100/10⁴ = 0.01 T

r = 9.11·10^-31·2.9·10⁷/(0.01·1.6·10^-19) = 0.0165 m = 1.65 cm