Electric Field

An electric field is the condition of space around a charge (or distribution of charges) in which another charge will feel a force. Electric field lines always point in the direction in which a positive charge would feel a force. For example, if we take a charge Q to be the source of an electric field E, and we bring a very small positive “test” charge q nearby to test the strength and direction of the electric field, then q will feel a force that is directed radially away from Q as shown below.

Electric field is the force per unit charge in a region of space.

The magnitude of the electric field is given by the equation

where electric field E is measured in newtons per coulomb, and F is the force acting on the charge q, which is feeling the force in the electric field. The test charge q would feel a force radially outward anywhere around the source charge Q, so we would draw the electric field lines around the positive charge Q like this:

Electric field lines are always drawn in the direction in which a positive charge will feel a force.

Electrons (negative charges) are moved when charge is transferred, but electric field lines are drawn in the direction a positive charge would move.

Remember, electric field lines in a region are always drawn in the direction in which a positive charge would feel a force in that region. They can also represent the path a positive charge would follow in that region. The diagrams below show how we would draw the electric field lines around a negative charge, two positives, two negatives, and a positive and a negative charge.

Example: A charge of +6 × 10⁻⁶ C is brought near a negative charge in a region where the electric field strength due to the negative charge is 20 N/C. What are the magnitude and direction of the force acting on the positive charge?

Solution: Electric field, force, and charge are related by the following equation, which can be solved for force:

F = qE = (6 × 10⁻⁶ C)(20 N/C) = 1.2 × 10⁻⁴ N

The force is directed radially inward toward the negative charge, since the positive charge is attracted to the negative charge.

Electric Potential

The electric potential V is defined in terms of the work we would have to do on a charge to move it against an electric field. For example, if we wanted to move a positive charge from point A to point B in the electric field shown below, we would have to do work on the charge, since the electric field would push against us.

Electric field is the force per unit charge, and electric potential is the work per unit charge.

We say that there is a potential difference ∆V between points A and B, and the equation for potential difference between two points is

and it is measured in joules/coulomb, or volts. When we apply potential difference to circuits in the next chapter, we will often call it voltage. If we place the charge q at point B and let it go, it would “fall” toward point A. We say that positive charges naturally want to move from a point of high potential (B) to low potential (A), and we refer to the movement of the positive charges as current. We will return to voltage and current in chapter 12.

Uniform Electric Field

We can create a uniform electric field in a region of space by taking two metal plates, setting them parallel to each other and separating them by a distance d, and placing a voltage V (as from a battery) across the plates so that one of the plates will be positive and the other negative.

Quick Quiz

True or False: A single positive charge creates a uniform electric field around itself.

Answer:

False. The electric field around a single positive charge gets weaker as you go farther from the charge, and therefore cannot be uniform.

The positive charges on the top plate will line up uniformly with the negative charges on the bottom plate so that each positive charge lines up with a negative charge directly across from it. This arrangement of charges creates electric field lines that run from the positive charges to the negative charges and are uniformly spaced to produce a uniform (constant) electric field everywhere between the plates. Conducting plates that are connected this way are called capacitors. Capacitors are used to store charge and electric field in a circuit that can be used at a later time. We will discuss capacitors further in chapter 12.

The electric field, voltage, and distance between the plates are related by the equation

It follows from this equation that the unit for electric field is volts/meter, which is equivalent to newtons/coulomb.

Example: Two charged parallel conducting plates are separated by a distance d of 0.005 m and are connected across a battery such that the electric field between the plates is 300 V/m.

• 1. What is the potential difference (voltage) of the battery that is connected across the plates?
  2. An electron is placed halfway between the plates. Describe the subsequent motion of the electron.
  3. A neutron is placed between the plates and near the top plate. Describe the force acting on the neutron at this location.

Solution:

• 1. (A) We are given the equation so it follows that
  V = Ed = (300 V/m)(0.005 m) = 1.5 volts.

This voltage is typical for most batteries you use each day, such as size AA, C, or D.

• 1. (B) A negatively charged electron would experience a force upward toward the positive plate, and therefore would accelerate upward. We could also say that the electron will move in a direction opposite to the direction of the electric field, since electric field lines are always drawn in the direction a positive charge would move.
  2. (C) Since a neutron has no charge, it will not experience a force from either the top or bottom plate, and consequently will not move.

Things to Remember

• Charge
  • The law of charges
• Coulomb’s law
• Separation and transfer of charge in an electroscope
• Electric field
  • Electric potential
  • Uniform electric field