Question

An electron moves in a circle of radius 20 cm with a velocity of 4.0 x 10⁶ m/s. Find the current at a point on the circle.

a) 5.0 A
b) 8.0 A
c) 12.0 A
d) 20.0 A

Answer 1

To find the current created by an electron moving in a circle, we calculate the period using the electron's velocity and the circle's circumference and then use the charge of an electron and the period to find the current.

Step-by-step explanation:

To calculate the current caused by the moving electron, remember that current (I) is defined as the rate of charge (Q) passing a point per unit time (t). Given that the electron completes one circular path, we can find the period (T) of the electron's motion, which is the time taken to complete one full circle, using the formula T = circumference/velocity = (2πr)/v. The charge of an electron is e = 1.6 × 10-19 C.

Using the given radius r = 0.2 meters and velocity v = 4.0 × 106 m/s, we find T = (2π×0.2 m)/(4.0 × 106 m/s). The current I will be I = e/T. Substituting the known values, we get the current as a single charge passing a point in one period of motion.