An electron with a negligible initial velocity enters the space between two plat

Question

An electron with a negligible initial velocity enters the space between two plate with the electric potential of 10000 V between them. It accelerates toward the other plate and passes through the opening A in it.
a). What is the electron's speed when it reaches point A?
b). On the other side of the plate there is a region with a constant magnetic field B = 0.1 T. The electron moves in a semi-circle and hits the plate at the point D. What is the distance between A and D?
c). How long does it take for the electron to travel that distance?
d). What is the direction of the magnetic field B? Draw on the picture

Explanation / Answer

A)

qV = mv^2/2

1.6*10^(-19) * 10000 = 9.1 * 10^(-31) v^2/2

v = 0.593*10^(8) m/s

B)

qvB = mv^2/r since magnetic forse is perendicular to velocity so that it can move in circular path

r = qvB / mv^2

= 1.6*10^(-19) * 5.93*10^7 * 0.1 / (2 * 1.6*10^(-19) * 10000)

= 2.965*10^(2) = 296.5 m

distance between A and D = diameter of circular path = 2r = 593 m

C)

t = v/2r = 5.93*10^7 / 593 = 10^(5) sec

D)

magnetic field is perpendicular to the velocity at point A

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