**Practice Problems: Gauss's Law**

Click here to see the solutions

1. (easy) A student measures the electric flux through a closed spherical surface of volume V to be X. She then removes the charge from inside the spherical surface and places it in a closed cylindrical surface of volume V/2. She then claims that the flux through the cylindrical surface is 2X. Explain why the student is wrong.

2. (easy) A pyramid with a 6.0 m square base has a height of 4.0 m. If it was placed in a vertical E-field (uniform magnitude of 52.0 N/C), determine the flux through one of the four sides.

3. (easy) A circular plane, with a radius of 2.2 m, is immersed in an E-Field with a magnitude of 800 N/C. The field makes an angle of 20° with the plane. What is the magnitude of the flux through the plane?

4. (easy) The net electric flux through an 3D closed surface is positive 2.2x10^{3} Nm^{2}/C. How much charge must be inside the surface? What is the sign on the charge?

5. (moderate) An imaginary rectangular shaped box is placed on the x-axis of a coordinate system. The left edge of the box is a distance of 0.4 m to the right of the origin. The box has a depth of 0.4 m, a width of 0.6 m, and a height of 0.4 m. A non uniform E-field (measured in N/C) passes through the box and varies along the x-axis according to the following:

E = (2.0x2 + 3.0) directed perfectly along the x-axis.

Determine the net flux through the surface.

6.(moderate) A Gaussian cube, 0.5 m along each edge, sits on the axis of a coordinate system such that three of its edges are along the postive x, y, and z axes. Determine the net electric flux through the top face of the cube if there is a uniform E-field of -0.5**i** + 0.3**j ** acting in that region of space.

7. (moderate) The concept of flux can also be applied to gravitational fields. Gauss's Law for gravity is:

(1/4πG)Φ_{g} = -m

where m is the mass contained within a Gaussian surface and the gravitational flux is

Φ_{g} = ∫**g·**d**A**

**g** is the gravitational field through the surface. Show that this law is equivalent to Newton's Law of Universal Gravitation.

**Please supplement these problems with those found in your companion text.**