An electron initially at rest is a accelerated by a voltage of 1.0 kV. It then e

Question

An electron initially at rest is a accelerated by a voltage of 1.0 kV. It then enters a uniform magnetic field directed perpendicular to the page, and moves in a clockwise circle of radius 25 cm in the plane of page. Find the kinetic energy and the speed of the electron (charge - 1.6 times 10^-19 C. mass 9.1 times 10^-31 kg) Find the magnetic field magnitude and direction. Find the frequency of circular motion If the electron is replaced with a proton of same speed, how will the radius change? Briefly explain, no calculation necessary.

Explanation / Answer

(a)
Kinetic Energy is given by,
K.E = q*V
K.E = 1.6 * 10^-19 * 1.0 * 10^3 J
K.E = 1.6 * 10^-16 J

K.E = 1/2*m*v^2
1.6 * 10^-16 = 1/2 * 9.1 * 10^-31 * v^2
v = 1.88 * 10^7 m/s

(b)
In Magnetic Field,
Magnetic Force = Centripetal Force
q*v*B = m*v^2/r
q*B = (m*v)/r
(1.6 * 10^-19 * B ) = (9.1 * 10^-31* 1.88*10^7 )/0.25
B = 4.28 * 10^-4 T

Direction :- Into the page.

(c)
f = 1/ ((2**0.25)/( 1.88 * 10^7))
f = 1.19 * 10^7 Hz

(d)
As the Charge is same, Speed is same, There will be no change in radius !!

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