(a) Twelve equal charges, q, are situated at the corners

Chapter 2, Problem 1P

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QUESTION:

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.

Questions & Answers

QUESTION:

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.

ANSWER:

Solution

Step 1 of 4

  1. 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 .


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