Problem 1P

(a) Twelve equal charges, q, are situated at the corners of a regular 12-sided polygon (for instance, one on each numeral of a clock face). What is the net force on a test charge Q at the center?

(b) Suppose one of the 12 q’s is removed (the one at “6 o’clock”). What is the force on Q? Explain your reasoning carefully.

(c) Now 13 equal charges, q, are placed at the corners of a regular 13-sided polygon. What is the force on a test charge Q at the center?

(d) If one of the 13 q’s is removed, what is the force on Q? Explain your reasoning.

Solution

Step 1 of 4

- We need to find out the net force on a test charge which is at the center of a regular sided polygon by equal charges which are kept at the corners of the sided polygon.

From the principle of superposition of charges, the net force on the charge is the sum of all forces by the charges acting at .

In this case the net force on charge is zero because all the forces will cancel out like force by charge at o'clock will cancel the force by charge at o'clock on the test charge .