24. Electric Force & Field; Gauss' Law

A uniform electric field $E$ points vertically upward. Cylinder (a) in Figure 1 is oriented so its axis is horizontal and its ends are perpendicular to the field lines. What is the net electric flux through cylinder (a)?

An infinite line of charge with linear charge density $\lambda$ passes along the axis of a cylindrical surface of radius $r$ and length $L$. What is the electric flux through the curved surface of the cylinder due to the line of charge?

A uniform electric field of magnitude $E$ points perpendicular to the plane of a circular loop of radius $r$. What is the electric flux $\Phi$ through the loop?

A uniform electric field of magnitude $E$ passes perpendicularly through a flat surface of area $A$. What is the electric flux $\Phi$ through the surface?

If a uniform electric field of magnitude $E$ passes perpendicularly through a flat surface of area $A$, the electric flux through the shaded surface is

Given three point charges enclosed by a closed surface $a_1$, what is the electric flux through the surface $a_1$ according to Gauss's law?

Given a uniform electric field $E$ perpendicular to the plane of an annular ring with inner radius $r_1$ and outer radius $r_2$, what is the electric flux $\Phi$ through the ring?

The electric flux through each surface of a cube is given below. Which surfaces of the cube does the electric field run parallel to? 

Φ₁ = 100 Nm² /C      Φ₄ = 0 Nm² /C

Φ₂ = 20 Nm² /C       Φ₅ = −40 Nm² /C

Φ₃ = 0 Nm² /C        Φ₆ = −80 Nm² /C

Where does the normal vector point for a spherical shell?

What is the total flux through the two surfaces depicted in the following figure? Note that surface 1 has an area of 50 cm² and surface 2 has an area of 100 cm² , and E = 500 N/C.

A uniform electric field points in the positive x direction and has a magnitude of 40N/C. What is the net flux through a cube with sides 4.0cm? The cube has one corner on the origin and the positive x, y, and z axes form three of its edges.

A hemispherical surface with radius $r$ in a region of uniform electric field $\overrightarrow{E}$ has its axis aligned parallel to the direction of the field. Calculate the flux through the surface.