Question

Draw some electric field lines and a few equipotential surfaces outside a positively charged metal cube. [Hint: What shape are the equipotential surfaces close to the cube? What shape are they far away?]

Short answer

Near the cube, equipotential surfaces are cube-like; far away, they are spherical.

Step-by-step solution

Understand the Electric Field

Begin by recognizing that electric field lines represent the direction of the force that a positive test charge would experience. For a positively charged metal cube, these field lines will originate from the surface of the cube and move outward into space.

Determine Shape of Equipotential Surfaces Close to the Cube

Equipotential surfaces are always perpendicular to electric field lines. Near a positively charged metal cube, these surfaces will mimic the shape of the cube. Therefore, close to the cube, the equipotential surfaces will appear as cubical shells or distorted cube-like shapes.

Consider the Shape of Electric Field Lines

Electric field lines will emerge perpendicular to the surface of the cube and will tend to diverge as they move farther from the cube, spreading out into the surrounding space.

Establish Equipotential Surfaces Far from the Cube

As you move further from the cube, the influence of its specific shape diminishes. Thus, the equipotential surfaces will tend to become more spherical, resembling the surface around a point charge due to symmetrical field distribution.

Draw the Diagram

On paper, draw the cube at the center. From the surface of the cube, sketch electric field lines radiating outward at various angles, tending to fan out as they extend. Around the cube, sketch surfaces that are roughly cube-shaped near the cube and transition to spherical shapes further away.

Key concepts

Equipotential Surfaces

Equipotential surfaces are regions in space where every point has the same electric potential. A helpful way to visualize them is to imagine drawing invisible contours, much like topographic lines on a map that indicate height. These surfaces are very important in electrostatics because they help illustrate where, and how, electric potential changes around objects.

• Near a positively charged metal cube, equipotential surfaces are shaped like the cube itself due to the strong and direct influence of the shape of the charge.
• As you move further away, these surfaces gradually transition into spherical shapes. This occurs because the effects of the cube's shape become less dominant, while the symmetry of the electric field increases.

Equipotential surfaces are perpendicular to electric field lines at every point. This is because work done by or against the electric field is zero when moving along an equipotential surface.

Electrostatics

Electrostatics is the branch of physics that studies electric charges at rest. It is concerned with understanding how charged particles interact and how these interactions can give rise to electric fields and potentials.

• One fundamental principle of electrostatics is that like charges repel each other, and unlike charges attract.
• In conductive materials, charges move freely, while in insulators, they are mostly fixed in place.
• Electrostatic principles help us to understand complex phenomena like the formation of electric fields around objects and the distribution of charge on conductive surfaces.

Understanding electrostatics is crucial for explaining how electric forces can influence the movement of charges, resulting in phenomena like the generation of electric fields and currents.

Electric Field Lines

Electric field lines provide a visualization of the electric field in a region of space. They display how a positive test charge would be influenced by the electric force if placed in the field.

• Electric field lines originate from positive charges and terminate at negative charges.
• The density of these lines indicates the strength of the electric field; closely packed lines mean stronger fields.
• Near a positively charged object like a metal cube, field lines will emerge perpendicularly and spread outward, illustrating how the electric field diminishes with distance.

These lines never cross each other, ensuring that the direction of the electric field is clear and unambiguous at all locations. By following the path of electric field lines, you can understand how a charge will be directed through space.