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## Electric Flux

Electric flux connects the geometry of conductors to the fields they generate. Learn this powerful tool and shortcut your way to the electric field of symmetrical arrangements like wires and sheets.

# Electric Flux

A square surface with side length $$3.7\text{ mm}$$ is located in a uniform electric field with magnitude $$E=2400\text{ N/C},$$ as shown in the above figure. The angle between the normal to the surface and the electric field is $$30^\circ.$$ What is the electric flux through the surface, assuming that the normal is directed outward?

An anemoscope is a device invented to show the direction of the wind, or to foretell a change of wind direction or weather. Consider a situation where an anemoscope is in a uniform electric field of magnitude $$E=4.5\text{ mN/C},$$ as depicted in the above figure. If the rim of the anemoscope is a circle with radius $$r=13\text{ cm},$$ and is perpendicular to the electric field, what is the electric flux through the fabric of the anemoscope?

A Gaussian cube of edge length $$1.0\text{ m}$$ is located in the $$xyz$$-space, as shown in the above figure. If the electric field in this space is expressed as $\overrightarrow{E}=4.0 \hat{i}-3.0(y^2+3.0) \hat{j} \text{ N/C},$ what is the electric flux through the top face of the Gaussian cube?

A cube with edge length $$0.90\text{ m}$$ is located in the $$xyz$$-space as shown in the above figure. If the uniform electric field in the space is given by $$-4.00 \hat{j} \text{ N/C},$$ what is the electric flux through the right face of the cube?

The above figure shows a Gaussian surface, which is in the form of a cylinder of radius $$R.$$ The Gaussian surface is located in a uniform electric field $$\overrightarrow{E},$$ where the axis of the cylinder is parallel to the electric field. What is the flux $$\Phi$$ of the electric field through this Gaussian surface, assuming that $$A$$ in the answer denotes the cap's area $$\pi R^2?$$

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