AP Physics C – Magnetic Fields – Free Response Practice Question on Magnetic Force on Moving Charges

“One of the deep secrets of life is that all that is really worth the doing is what we do for others.”

– Lewis Carroll

 

The cathode ray oscilloscope is one of the most versatile instruments which is used as a test instrument in a variety of forms in almost all fields of scientific activity. Most of you may be familiar with this impressive instrument which is essentially a highly evacuated glass bulb containing an electron gun and a fluorescent screen, with provisions for deflecting the electron beam, usually by applying voltages across deflecting plates. I give below a free response question related to the cathode ray tube:

The adjoining figure represents a cathode ray tube in a cathode ray oscilloscope. The voltage applied (with respect to the cathode) to the final accelerating anode is V and the distance between the anode and the fluorescent screen of the cathode ray tube is L. The mass of the electron is m and the magnitude of its charge is e.  The cathode ray tube is so oriented that in the undeflected condition the electron beam is horizontal and is along the magnetic meridian, with the electrons traveling from south to north. The horizontal component of the earth’s magnetic field at the place is B_h. Now, answer the following questions:

(a) Calculate the velocity with which the electrons strike the fluorescent screen, assuming that the space between the accelerating anode and the fluorescent screen is devoid of electric fields and the electrons start from the cathode with negligible speed.

(b) The cathode ray tube is rotated through 90º about a verti8cal axis so that the electrons travel from east to west. In what direction will the spot of light (produced by the impact of the electron beam) on the fluorescent screen be deflected? Select the correct option from the following, by putting a tick mark (√) against one of the following:

Upwards………

Downwards………

Leftwards………

Rightwards……..

Justify your answer.

(c) If the cathode ray tube is rotated through 90º in the opposite direction, will the direction of deflection of the spot of light on the screen change? Justify your answer.

(d) Derive an expression for the specific charge (charge to mass ratio) of the electron in terms of the given data and the shift s of the electron spot on the screen, on rotating the cathode ray tube through 90º. Assume that the shift s is small compared to the distance between the accelerating anode and the fluorescent screen.

Try to answer this question. You are required to answer it within 15 minutes and it carries 15 points.

I’ll be back soon with a model answer for your benefit.