Challenge - Symmetry

Section 22.7 Challenge - Symmetry

Explanation 22.7.1. Flux Practice.

Figure 22.7.1. Two points and an imaginary square loop.
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The figure above shows an imaginary square loop centered between two points \(A\) and \(B\text{.}\)

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(a)

Choose an area vector for the loop.

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(b)

Suppose a point charge \(+Q_o\) is located at point \(A\text{.}\) Is the electric flux through the loop positive, negative, or zero?

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(c)

Suppose a point charge \(+Q_o\) is located at point \(A\) and a point charge \(+2Q_o\) is located at point \(B\text{.}\) Is the electric flux through the loop positive, negative, or zero?

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(d)

Suppose a point charge \(+Q_o\) is located at point \(A\) and a point charge \(-2Q_o\) is located at point \(B\text{.}\) Is the electric flux through the loop positive, negative, or zero?

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Explanation 22.7.2. Flux.

Figure 22.7.2. Two point charges and a Gaussian cube.
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Two positive point charges \(+q\) are located a distance \(L\) apart, as shown above. A Gaussian surface (a cube with side length \(L\)) is drawn with its center at the location of the left charge.

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(a)

Is the electric flux through the right face of the cube positive, negative, or zero?

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(b)

Suppose the charge on the right were replaced by a charge of \(-q\text{.}\) Would the net electric flux through the entire cube increase, decrease, or stay the same?

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Subsection Metacognitive Reflection

A major theme of this unit was determining how and when symmetry can help make your calculations easier. Write a short paragraph summarizing symmetry and how it can be useful when calculating the electric field. Which activities did you complete this week that you want to remember?

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