You observe an electron moving on your test paper in a clockwise circle of radiu

Question

You observe an electron moving on your test paper in a clockwise circle of radius H. 9.7cm, at a constant speed of L 5.1 times 10^6 m/s Suppose that the electron's circular motion is due to the presence of a uniform magnetic field. What must be the magnitude and direction of this magnetic field? : Answer: times 10 T (for the magnitude) Answer for direction: choose from the following six possibilities and circle the correct one... Toward the top of the page Toward the bottom of the page To the left To the Right Toward you Away from you Suppose instead that the electron's circular motion is due to the presence of a stationary charged particle located at the center of the circle. What is the value of this stationary charge? Make sure to specify the correct sign on the charge in your answer. Answer: times 10 C

Explanation / Answer

Given radius of the circle r = 9.7 cm = 0.097 m , speed of the electron v = 5.1*10^6 m/s

if the electron is in circular motion due to the magnetic field seems to be cyclotron motion problem

Bqv Sin theta = mv^2 /r            

                                B magnetic field, r radius, v speed of electron, m mass of electron =9.1*10^-31kg     

B= (m*v / r*q*Sin theta)    

= (9.1*10^-31*5.1*10^6 / (0.097*-1.6*10^-19*Sin90))    

= - 2.9903*10^-4 T

direction is towards the bottom of the page

b) suppose the electron is in circular motion due to a charge at centre the charge at at the centre

   from Coulomb force between two charges is equal to the centripetal force

i.e k Qe/r^2 = mv^2/r

         Q = m*v^2*r / k*q

             = 9.1*10^-31*(5.1*10^6)^2*0.097/ (9*10^9*-1.6*10^-19)

        Q      = -1.5943*10^-9 C

so the charge at the centre is - 1.5943*10^-9 C,

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