Electrostatics- AP Physics C Free Response Practice Question on Electric Field & Potential

Essential points to be remembered in respect of electric field and potential were discussed on this blog on 16^th June 2008. You can access that post by clicking here.

All posts related to electrostatics can be accessed by clicking on the label ‘electrostatics’ below this post.

Today I’ll give you a free response practice question involving electric field and potential:

A quantity Q of positive charge is placed at the position A (Fig.) on a circular conducting ring of radius R made of thin uniform wire. The system is placed in a region of space where the effect of external charges is negligible. Now, answer the following questions in respect of the above system, assuming the expressions for the electric field and potential due to a point charge:

(a) What is the electric field at the centre of the ring? Justify your answer.

(b):

(i) What is the electric potential at the centre of the ring?

(ii) If the charge placed on the ring is negative, will there be any change in the electric potential at the centre of the ring? Justify your answer.

(c) Derive an expression for the electric potential at a point such as P on the axis of the positively charged ring. (Assume that the axis of the ring is along the x-direction and the centre of the ring is at the origin).

(d):

(i)Using the expression for the electric potential obtained in part (c) above, obtain an expression for the electric field at the point P on the axis of the ring.

(ii) Show that the electric field on the axis is maximum at a distance R/√2 from the centre

(e) Show qualitatively, in a diagram, the nature of variation of the electric field along the axis of the ring, covering both sides of the ring.

This question carries 15 points and you have 15 minutes for answering it. Try to answer this question. I’ll be back soon with a model answer for your benefit.