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Four point charges are located at the corners of a square

Chapter 19, Problem 38P

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QUESTION:

Four point charges are located at the corners of a square with sides of length a. Two of the charges are \(+q\), and two are \(-q\). Find the magnitude and direction of the net electric force exerted on a charge \(+Q\), located at the center of the square, for each of the following two arrangements of charge:

(a) The charges alternate in sign \((+q,-q,+q,-q)\) as you go around the square;

(b) the two positive charges are on the top corners, and the two negative charges are on the bottom corners.

Questions & Answers

QUESTION:

Four point charges are located at the corners of a square with sides of length a. Two of the charges are \(+q\), and two are \(-q\). Find the magnitude and direction of the net electric force exerted on a charge \(+Q\), located at the center of the square, for each of the following two arrangements of charge:

(a) The charges alternate in sign \((+q,-q,+q,-q)\) as you go around the square;

(b) the two positive charges are on the top corners, and the two negative charges are on the bottom corners.

ANSWER:

Step 1 of 4

(a)

Here we need to calculate the magnitude and direction of net electrostatic force experienced by a charge \(+Q\) which is located at the center of the square, for the given charge configuration.

The charges configuration as we go around the square, the charges have alternate polarity with sign \((+q,-q,+q,-q)\).

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