Chapter 24, Problem 1CQ

Suppose you have the uniformly charged cube in FIGURE Q24.1. Can you use symmetry alone to deduce the shape of the cube 's electric field? If so, sketch and describe the field shape. If not, why not?

To determine

If symmetry alone can be used to deduce the shape of the cube’s electric field.

Explanation of Solution

Given:

The following figure of uniformly charged cube is given.

  

Using Gauss’s law, we can deduce electric fields, particularly those with a high degree of symmetry, simply from the shape of the charge distribution.

The pattern of the electric field through the surface is like that the shape of the charged body, if the Gaussian surface matches the symmetry of the charge dispersion inside. For a consistently charged dispersion, the shape of the Gaussian surface coincides with the shape of the electric field. So, the shape of the electric field is cubical in nature for a consistently charged cube shape that is the electric field at each point on the face of a solid shape is comparative and its direction is perpendicular to the face cube. The sketch of the electric field through each face of the consistently charged cube is appeared as follows.

  

Conclusion:

We can use the symmetry alone to predict the shape of the electric field, the electric field in each face of the cube will have the same magnitude and perpendicular to that face.