magnetic fields An electron acquires a certain kinetic energy as it is accelerat

Question

magnetic fields

An electron acquires a certain kinetic energy as it is accelerated from rest through an electric field from point A to C, as shown below. It then enters an area with a magnetic field oriented in the plane perpendicular to the page (it is not known whether the field is oriented into the page or out of the page). After half a circular turn, the electron leaves the magnetic field, travelling in the direction exactly opposite to its entry direction. At this time, the speed of the electron is 1.83 times 10^7 m/s. The distance between points C and D is 4.00 cm. a) What is the magnitude and direction of the magnetic field? b) What is the magnitude of voltage V_AC that was applied between points A and C? c) What is the magnitude and direction of the electric field (between A and C) if the distance AC is 5.00 cm?

Explanation / Answer

a)

For circular motion, magnetic force will provide the necessary centripetal force

So, qvB = mv^2/R

So, B = mv/qR

= 9.1*10^-31*(1.83*10^7)/(1.6*10^-19*0.02)

= 5.210^-3 T <------ magnitude of magnetic field

Direction of magnetic field = into the page

b)

KE gained from A to C = Work done by Electric field

So, 0.5*mv^2 = Vq

So,V = mv^2/2q = 9.1*10^-31*(1.83*10^7)^2/(2*1.6*10^-19)

= 952.3 V <------- answer

c)

V = E*d

So, E = V/d

= 952.3/0.05 = 19046 N/C <-------answer

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