Question

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?

Short answer

To determine if symmetry can alone be used to deduce the shape of the cube's electric field

Step-by-step solution

Definition of Electric Field 

Electric field (E) is defined as the physical field surrounding electrically charged particles and which exerts force on all the other charged particles within the field by either attracting or repelling them.

Deducing the shape of the cube's electric field using symmetry

Electric field can be deduced using Gauss's law, particularly for the ones that have high degree of symmetry from the shape of charge distribution.

The pattern of the electric field is somewhat similar to the shape of the charged body we have if the gaussian surface matches the symmetry of the charge dispersion that is inside.

Sketching the field shape

Here the shape of the electric field is cubical in nature and therefore the electric field at each point on the face is comparative and its direction is perpendicular to the face cube.

The sketch therefore is:

Final Answer

Yes we can deduce the shape of the cube’s electric field by using symmetry alone. Herein, the electric field in each face of the cube will have same magnitude and perpendicular to that face.