Question

Draw some electric field lines and a few equipotential surfaces outside a positively charged conducting cylinder. What shape are the equipotential surfaces?

Short answer

Describe the electric field lines and equipotential surfaces for a positively charged conducting cylinder. The electric field lines for a positively charged conducting cylinder are straight, evenly spaced, and point outward in all directions, originating from the surface of the cylinder. Equipotential surfaces are surfaces with the same electric potential, and they are always perpendicular to the electric field lines. In this case, the equipotential surfaces are concentric cylinders around the charged cylinder, having the same shape as the charged cylinder, with decreasing distance between them as they move farther away from the charged cylinder. This indicates that the electric potential decreases as we move away from the positively charged conducting cylinder.

Step-by-step solution

Drawing the positively charged conducting cylinder

First, draw a positively charged conducting cylinder in the center of your page. Label it with a "+" sign to indicate that it has a positive charge.

Drawing electric field lines

Now, draw the electric field lines originating from the charged cylinder. The electric field lines should be straight and evenly spaced, pointing outward in all directions. Start from the surface of the cylinder and continue them to the edges of the page. The electric field lines represent the path that a positive test charge would follow if placed in the electric field.

Drawing equipotential surfaces

Draw a few equipotential surfaces around the positively charged cylinder. Equipotential surfaces are surfaces with the same electric potential, and they are always perpendicular to the electric field lines. In this case, the equipotential surfaces will be concentric cylinders around the charged cylinder. The distance between these equipotential surfaces will decrease as you move away from the charged cylinder, indicating that the electric potential is decreasing.

Identifying the shape of the equipotential surfaces

The equipotential surfaces outside the positively charged conducting cylinder are concentric cylindrical surfaces. These surfaces have the same shape as the charged cylinder and are evenly spaced in regions close to the charged cylinder.

Understanding the relationship between electric field lines and equipotential surfaces

The electric field lines and equipotential surfaces are always perpendicular to one another. This is because the electric field is always directed in the direction of the steepest decrease in electric potential. By understanding this relationship, we can infer that the electric potential decreases as we move away from the positively charged conducting cylinder.