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spaghetti3451

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## Homework Statement

This problem is taken from 'Introduction to Electrodynamics' by David Griffiths.

(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 on "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.

## Homework Equations

3. The Attempt at a Solution [/B]

(a) Zero, because each of pair of opposite charges exert forces on ##Q## of equal magnitude in opposite directions.

(b) The force on ##Q## is given by Coulomb's law, and acts in the direction of "6 o'clock."

(c) This is where I've got stuck. I picture one charge ##q## at the 12 o'clock position, and the others spread symmetrically throughout the rim of the clock face. Then, I have a gut feeling that the net force is due only to the charge at the 12 o'clock position. Using the above picture of the position of the charges, the horizontal components of the forces cancel by symmetry. However, I'm unable to account for the cancellation of the vertical forces due to the other 12 charges.

Thoughts?

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