6.1 Electric Flux

What angle should there be between the electric field and the surface shown in the figure in the previous example so that no electric flux passes through the surface?

If the electric field in the example is $\overset{\rightarrow}{\text{E}} = m x \hat{\text{k}} ,$ what is the flux through the rectangular area?

Discuss how to orient a planar surface of area A in a uniform electric field of magnitude $E_{0}$ to obtain (a) the maximum flux and (b) the minimum flux through the area.

The net electric flux crossing a closed surface is always zero. True or false?

Calculate the flux through the sheet of the previous problem if the plane of the sheet is at an angle of $60 °$ to the field. Find the flux for both directions of the unit normal to the sheet.

The electric flux through a square-shaped area of side 5 cm near a large charged sheet is found to be $3 \times 10^{−5} \text{N} \cdot \text{m}^{2} / \text{C}$ when the area is parallel to the plate. Find the charge density on the sheet.

A square surface of area $2 \text{cm}^{2}$ is in a space of uniform electric field of magnitude $10^{3} \text{N}/\text{C}$. The amount of flux through it depends on how the square is oriented relative to the direction of the electric field. Find the electric flux through the square, when the normal to it makes the following angles with electric field: (a) $30 °$, (b) $90 °$, and (c) $0 °$. Note that these angles can also be given as $180 ° + \theta$.

Consider the uniform electric field $\overset{\rightarrow}{\text{E}} = \left(4.0 \hat{\text{j}} + 3.0 \hat{\text{k}}\right) \times 10^{3} \text{N}/\text{C} .$ What is its electric flux through a circular area of radius 2.0 m that lies in the xy-plane?

An infinite charged wire with charge per unit length $\lambda$ lies along the central axis of a cylindrical surface of radius r and length l. What is the flux through the surface due to the electric field of the charged wire?