Electric Fields

The gravitational and electric forces can act through space without any physical contact between the interacting objects. Just like the gravitational force the electric force is associated with a field. The electric field represents a alteration of the space surrounding an electric charge such that a second charge placed in the field will experience an electric force. The electric field vector, E specifies the magnitude and direction at any point in the electric field. The magnitude and direction of the electric field vector at some point in an electric field is defined to be the magnitude and direction of the electric force exerted on a positive test charge placed at that point divided by the test charge.

The electric force on another electric charge, q 1, placed in the field is then given by: If the charge q 1 is positive, the direction of the force is the same as the field. If q 1 is negative the direction of the force is opposite to the direction of the field. From Coulomb’s Law we can derive an expression for the electric field due to a point charge, q 1. The force on a positive test charge, q o due to q 1 is: The electric field due to q 1 is then:

The electric field points away from a positive source charge and toward a negative source charge. The electric field at a point P due to more than one charge is the vector sum of the individual fields produced by each charge. Where r i is the distance from the source charge q i to point P.

Three point charges, q 1 = 25  C, q 2 = -40  C, and q 3 = 60  C lie on a straight line as shown below. What is the magnitude and direction of the electric field at point P, 5.5m from the origin? The electric field at point P due to q 1 points away from q 1. The electric field at point P due to q 2 points toward q 2. The electric field at point P due to q 3 points away from q 3.

The negative sign indicates that at point P the direction of the electric field is to the left.

Two point charges, q 1 = 25  C and q 2 = -40  C lie on a straight line as shown below. For the electric field to be zero the fields due to q 1 and q 2 must cancel. To cancel the fields must be equal in magnitude and opposite in direction. There are three possibilities for the location of a point where the electric field is zero. 1. To the right of q 2, x > 4m. 2. Between q 1 and q 2, 0 < x < 4m. 3. To the left of q 1, x < 0. E 1 and E 2 are opposite but q 2 > q 1 and r 1 > r 2 therefore E 1 and E 2 can not be equal in magnitude and can not cancel. E 1 and E 2 are not opposite and can not cancel. E 1 and E 2 are opposite, q 2 > q 1 and r 1 < r 2 therefore E 1 and E 2 can be equal in magnitude and can cancel. Is there a point where the electric field is zero?

Consider two parallel sheets separated by a distance d and having equal areas, A. The sheets carry equal but opposite electric charges. This charge distribution is called a parallel plate capacitor. At every point between the plates of the capacitor the electric field is the same and directed from the positive plate toward the negative plate. Where  o is the permittivity of free space:

A parallel plate capacitor is composed of plates each with an area of 0.002m 2 and separated by a distance of 0.3m. They carry equal and opposite charges of 0.8  C. A proton, m p =1.67 x kg, q p =+1.6x C is released from rest at the positive plate. What will be the velocity of the proton when it reaches the negative plate?

This velocity is approximately 17% of the speed of light!

How long did it take the proton to cross the capacitor?