AP Physics C - Free Response Practice Question on Electrostatic Potential Energy

“I believe in standardizing automobiles, not human beings.”

– Albert Einstein

Today I’ll give you a free response practice question involving electrostatic potential energy. You may answer it yourself so that you will realize your strength and weakness in answering free response questions within the stipulated time. Of course, I’ll give you a model answer later, as usual.

Here is the question:

A thin circular ring of radius R has positive charges sprayed uniformly along it so that the linear charge density along it is λ. The ring is located in the y-z plane with its centre at the origin of a right handed Cartesian co-ordinate system, in a space lab, where the effect of gravity is negligible. From the point P [–(√15)R, 0, 0] shown in the figure, a particle of mass m and charge +q is projected with speed v along the positive x-direction. Now answer the following:

(a) Which one of the following statements (i), (ii) and (iii) regarding the electric field vector at P (due to the charges on the ring) is correct? [Put a tick (√) mark against your choice].

(i) Electric field at P is along the positive x-direction ……..

(ii) Electric field at P is along the negative x-direction ……..

(iii) Electric field at P is zero ……..

Justify your answer.

(b) Determine the electrostatic potential energy of the charge q when it is located at P.

(c) Determine the electrostatic potential energy of the charge q when it is located.at the centre of the ring.

(d) Determine the minimum value of the speed of projection for the charged particle to pass through the ring.

(e) Explain what happens to the charged particle if the speed of projection is less than the minimum value mentioned in part (d) above.

The above question is worth 15 points and you may take about 15 minutes for answering it. Try to answer it. I’ll be back soon with a model answer for your benefit.