Module 4 The Electric Field Revisited

Electric Fields and Conductors

Electric fields in the presence of conductors have several unique and not necessarily intuitive properties.

Learning Objectives

Describe unique properties expressed by electric fields in the presence of conductors

Key Takeaways

Key Points

There is no electric field inside a charged conductor. This is because charges, which are located on the surface of the conductor, symmetrically oppose one another and sum to 0 in all locations.
Charged surfaces align themselves perpendicularly relative to electric fields to achieve electrostatic equilibrium. If charges are not distributed as such, they will exert net force upon one another, which will move them. In such an instance, the charges will not be at static equilibrium.
Curvature on the surface of a field allows for increased charge concentration. Much of the repulsion charges exert is in the direction moving away from the surface of the conductor, rather than along its surface. Charges thus push one another more weakly along the surface of a curved conductor.

Key Terms

vector field: a construction in which each point in a Euclidean space is associated with a vector; a function whose range is a vector space
equilibrium: The state of a body at rest or in uniform motion, the resultant of all forces on which is zero.

An electric field, like other fields (e.g., gravitational or magnetic), is a vector field that surrounds an object. Electric fields are found around electric charges and help determine the direction and magnitude of force the charge exerts on a nearby charged particle. It measures units of force exerted per unit of charge, and its SI units are N/C.

Field Lines Created by a Point Charge: Lines around the positive charge represent the electric field it creates.

Electrical conductors are materials in which internal charges can move freely. Therefore, they can facilitate the flow of charge, or current. When a conductor is placed in the presence of an electric field, it exhibits some interesting properties:

There is no electric field inside a charged conductor. A charged conductor at electrostatic equilibrium will contain charges only on its outer surface and will have no net electric field within itself. This is because all the charges in such a conductor will symmetrically oppose other charges within the conductor, causing the net result to sum to 0.
Charged surfaces align themselves perpendicularly relative to electric fields. Provided a conductor is at electrostatic equilibrium, the electric field upon the surface will be aligned perpendicularly with respect to that surface. If there were a nonzero parallel component of the electric field, with respect to any charge on the surface of a conductor, that charge would exert a force and would move. If the conductor is at equilibrium, such a force cannot exist, and therefore the direction of the electric field must be completely perpendicular to the surface.
Curvature on the surface of a conductor allows for increased charge concentration. Charge will not necessarily distribute itself evenly over the surface of a conductor. If the surface of the conductor is flat, charge will be very evenly distributed. But as the surface becomes more sharply curved, charge can be found more densely packed in areas, even if the conductor is at electrostatic equilibrium. Charges on a curved surface repel one another less strongly than they would on a smooth surface. This is because, based on how the charges are positioned, much of the repulsion the charges exert is in the direction away from the surface of the conductor, not along its surface. And it is harder for charges to be pushed off a surface than along it. Therefore, the repulsion between charges on a curved surface is weaker.

Electrical Charge at a Sharp Point of a Conductor: Repulsive forces towards the more sharply curved surface on the right aim more outward than along the surface of the conductor.

Conductors and Fields in Static Equilibrium

In the presence of charge or an electric field, the charges in a conductor will redistribute until they reach static equilibrium.

Learning Objectives

Describe behavior of charges in a conductor in the presence of charge or an electric field and under static equilibrium

Key Takeaways

Key Points

The presence of charge or an electric field will force charges in a conductor to redistribute along the conductor’s surface until static equilibrium is achieved.
At static equilibrium, charge will be more concentrated in sharp, pointy areas of conductors than elsewhere.
At static equilibrium, the inside of a conductor will be entirely shielded from an external electric field.

Key Terms

static equilibrium: the physical state in which all components of a system are at rest and the net force is equal to zero throughout the system

Conductors are materials in which charges can move freely. If conductors are exposed to charge or an electric field, their internal charges will rearrange rapidly. For example, if a neutral conductor comes into contact with a rod containing a negative charge, some of that negative charge will transfer to the conductor at the point of contact. But the charge will not stay local to the contact point — it will distribute itself evenly over the surface of the conductor. Once the charges are redistributed, the conductor is in a state of electrostatic equilibrium. It should be noted that the distribution of charges depends on the shape of the conductor and that static equilibrium may not necessarily involve an even distribution of charges, which tend to aggregate in higher concentrations around sharp points. This is explained in.

Electrical Charge at a Sharp Point of a Conductor: Forces between like charges at either end of the conductor are identical, but the components of the forces parallel to the surfaces are different. The component parallel to the surface is greatest on the flattest surface and therefore moves charges away from one another more freely. This explains the difference in concentration of charge on flat vs. pointed areas of a conductor.

Similarly, if a conductor is placed in an electric field, the charges within the conductor will move until the field is perpendicular to the surface of the conductor. Negative charges in the conductor will align themselves towards the positive end of the electric field, leaving positive charges at the negative end of the field. The conductor thus becomes polarized, with the electric field becoming stronger near the conductor but disintegrating inside it. This occurrence is similar to that observed in a Faraday cage, which is an enclosure made of a conducting material that shields the inside from an external electric charge or field or shields the outside from an internal electric charge or field.