How Does Electric Field Orientation Affect Flux Through a Cylinder?

[smahapatra3]

Homework Statement

The electric field is measured all over the surface of a cylinder whose diameter is 8 cm and whose height is 20 cm, as shown in the diagram. At every location on the surface the electric field points in the same direction (+y). E1 is found to be 533V/m; E2 is 730V/m; E3 is 1226V/m.

http://www.webassign.net/mi3/22.P.015.alt01-CylinderE_2.gif

Which of the following statements are true?
1. This is an impossible pattern of electric field.
2. Only the curved surface of the cylinder gives a nonzero contribution to the net electric flux.
3. The flux on the flat ends of the cylinder is 0.
4. Not enough information is given to solve this problem.
5. The angle between E1 and is 90 degrees.
6. The angle between E2 and is 90 degrees.
7. The net flux on this cylindrical surface is negative.

Homework Equations

Gauss's Law

The Attempt at a Solution

1 is wrong because something other than the cylinder is causing the electric field. I 2 is wrong because no part of the cylinder contributes to the electric field. So that makes 3 right. I'm not sure about 5 or 6. I know 7 is right.

 

[anathema]

I would like to clarify and provide additional information to help answer this question accurately.

Firstly, it is important to note that the electric field is a vector quantity, meaning it has both magnitude and direction. In this case, the electric field is pointing in the +y direction at every location on the surface of the cylinder.

Now, let's review the statements one by one:

1. This is an impossible pattern of electric field.

This statement is incorrect. It is possible for the electric field to have a constant magnitude and direction at every point on the surface of a cylinder. This can occur if there is a uniform charge distribution inside the cylinder, or if the cylinder is placed in a uniform electric field.

2. Only the curved surface of the cylinder gives a nonzero contribution to the net electric flux.

This statement is also incorrect. According to Gauss's Law, the net electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. In this case, since the electric field is constant and perpendicular to the surface, the net electric flux through the entire surface of the cylinder will be nonzero.

3. The flux on the flat ends of the cylinder is 0.

This statement is correct. The electric field is perpendicular to the flat ends of the cylinder, so there is no component of the electric field that is parallel to the surface. Therefore, the electric flux through the flat ends will be zero.

4. Not enough information is given to solve this problem.

This statement is also incorrect. We have been given all the necessary information (electric field values, dimensions of the cylinder) to solve this problem using Gauss's Law.

5. The angle between E1 and is 90 degrees.

This statement is incorrect. Since the electric field is pointing in the +y direction at every point on the surface of the cylinder, the angle between E1 and the surface will be 0 degrees.

6. The angle between E2 and is 90 degrees.

This statement is also incorrect. The angle between E2 and the surface will also be 0 degrees, as the electric field is perpendicular to the surface.

7. The net flux on this cylindrical surface is negative.

This statement is incorrect. The net flux on the cylindrical surface will be positive, as the electric field is pointing in the same direction (+y) at every point on the surface. The negative sign in Gauss's Law is used to indicate