AP Physics C - Free Response Practice Question on Electrostaics

“There is no substitute for hard work”.

– Thomas A. Edison

I give below a free response practice question on electrostatics for the benefit of AP Physics C aspirants. The question is meant for checking your understanding and the capacity of application of the concepts of electric potential, electric potential energy and the law of conservation of energy. Here is the question:

A thin circular nonconducting disc of radius ‘a’ resting horizontally on the ground has positive charges sprayed on its top surface so that it has a uniform surface charge density σ. The centre of the disc is O and the axis of the disc is vertical (Fig.). There are no other electric charges in the vicinity for producing any appreciable interaction on the charges on the disc and the acceleration ue to gravity at the place is g. Now answer the following questions:

(a) Derive an expression for the electric potential at a point on the axis of the disc at distance x from its centre.

(b) What is the electric potential at the centre of the disc?

(c) A positively charged particle of mass m and charge q with specific charge (q/m) of 8ε₀g/σ is released from rest from a point P on the axis of the disc. The distance of point P from the centre of the disc is d. If the particle just reaches the centre O of the disc, determine the value of d.

(d) Explain qualitatively the nature of motion of the charged particle after its release from the point P stated in part (c) above.

Try to answer this question. This carries 15 points and you can take 15 minutes to answer it. I’ll be back soon with a model answer for you so that you can compare your answer with it and get an idea of your strength and weakness.