2. In case A at right, a point charge +q is a Case A Case B +q Uniformly distanc

Question

2. In case A at right, a point charge +q is a Case A Case B +q Uniformly distance s from the center of a small ball with charge +Q charged rod with total In case B the +q charge is a distance s from charge +0 the center of an acrylic rod with a total charge +Q Consider the following student dialogue Student 1 The charged rod and the charged ball have the same charge, +Q, and are the same distance from the point charge, +q. So the force on +q will be the same in both cases." Student 2 "No, in case B there are charges spread all over the rod. The charge directly below the point charge will exert the same force on +q as the ball in case A. The rest of the charge on the rod will make the force in case B bigger." Neither student is correct. Describe the errors made by each student.

Explanation / Answer

Take L as the length of the rod = L
Electric field due to the point charge = kQ/s2.
Electric field due to uniformly charged rod = kQ/{s x[ sqrt(s2 + (L/2)2]}
These two equations will be same only if L becomes zero, that is when the rod become a point charge.

Student 1 is incorrect since the field produced by the two charge configurations are different.
Student 2's argument that the charge directly below the point charge exerts the same force in both case is incorrect because there is only Q/L charge in the case of rod but whole Q charge in the case of point charge. The force in case B is more is also incorrect because if we compare the equations of the electric field, the field produced by the rod is less and so is the force.

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