Electricity and Magnetism

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 magnitude of 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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