Problem 3 The electrons in the beam of a television tube have an energy of 17 ke

Question

Problem 3 The electrons in the beam of a television tube have an energy of 17 keV. The tube is oriented so that the electrons move horizontally from west to east. The vertical component of the Earth's magnetic field at the location of the television has a magnitude of 59.0 uT and is pointing down. a) In which direction does the force on the electrons act (enter N for north, S for South, E for East, or w for West)? Neglect a possible horizontal component of the magnetic field. Submit Answer Tries 0/6 b) What is the magnitude of the acceleration due to the vertical component of the Earth's magnetic field of an electron in the beam? Submit Answer Tries 0/6 c) If the inclination of the earth's magnetic field near the TV is 17deg, calculate the magnitude of the force on the electrons due to the horizontal component of the Earth's magnetic field. Submit Answer Tries 0/6

Explanation / Answer

a)The electron experiences a velocity dependent force, the Lorentz force, which is perpendicular to both the direction of the velocity and to the magnetic field direction. The right hand rule states that, to find the direction of the magnetic force on a positive moving charge, the thumb of the right hand point in the direction of v, the fingers in the direction of B, and the force (F) is directed perpendicular to the righthand palm.

So, the elctrons will be deflected towards South.

b)To find the acceleration of an electron, we must use a = v2/ r. To find v2, we use 2*KE / m. To find the radius, we use r = m*v / q*B.

The mass of an electron is 9.11 x 10-31 kg. The charge of an electron is 1.6 x 10-19 C, which is the absolute value.

v2= [ 2 x (2.7237x10-15J) ] / 9.11 x 10-31 kg = 5.98 x 1015 m-2s-2

v = (5.98 x 1015)1/2 = 7.73 x 107 m/s

Now for r,

r = [ (9.11 x 10-31 kg) x (7.73 x 107 m/s) ] / [ (1.60 x 10-19 C) x (5.9 x 10-5 T) ] = 7.46 m

a = v^2 / r = (5.98 x 1015 m^2/s^2) / 7.46 m

= 8.02 x 1014 m/s2

c) The magnetic force= qvB sin (theta),

where theta= angle of inclination of earth's magnetic filed=90-17=73o

So, FB= (-1.60 x 10-19 C)(7.73 x 107 m/s)(5.9 x 10-5 T)sin(73o)

= 4.93x10-16 N

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