Chapter 12 Electric Fields



		1. Gravitational Field vs. Electric Field 2. Electric Field Line 3. Gravitational Potential vs. Electric Potential 4. Chapter Quiz
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Section 1. Gravitational Field vs. Electric Field

Let us have your opinion about the attraction of an object.

Gravitatoinal Force

The concept of electric field was introduced by Michael Faraday. The electrical field force acts between two charges, in the same way that the gravitational field force acts between two masses. We know about accelaration of the earth, i.e., the gravity (g = 9.8 m/s^²), but where does this number come from?

It comes from Newton's law of universal gravitation. It states that every matter which has a mass attracts other matters with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between the centers of gravity of the two matters.

where:

or (constant),
m_e = mass of the earth (kg),
m_o = mass of an object (kg), and
d = distance between the earth and the object (m).

We already studied about gravitational force of an object on earth, which is F = m*g, where "m" is mass of the object and "g" is the gravity of the earth. Then, we can say that . Therefore, gravity (g) of the earth is , where "m_e" is the mass of the earth and "d" is its radius (we are talking about gravitational force on the surface of the earth.).

Value of g

The electric field (E) is derived in the same way from the equation

(see right)

where:

(constant),
Q = electric force of one object (C),
q = electric force of the other object (C), and
d = distance between the two objects (m).

However, electric field E is a little bit different from gravitational field g. Gravitational force depends on mass, whereas electric force does not depend on mass. Instead, electric force depends on charges on both objects.

By rearranging the formula, we get:

Electric field (E) for Q:
Electric field for q:

Let's divide the electric force (F) by charge q:

Therefore, the electric field tells us the force per unit charge.

Section 2. Electric Field Line

	Electric field lines can be drawn using field lines. They are also called force lines.
	(Positive charge electric field)	The field lines are originated from the positive charge.	(Negative charge electric field)	The field lines end up at the negative charge.

A positive charge exerts out and a negative charge exerts in equally to all directions; it is symetric. Field lines are drawn to show the direction and strength of field. The closer the lines are, the stronger the force acts on an object. If the lines are further each other, the strength of force acting on a object is weaker.

Example problem 1.

What are the magnitude and direction of the electric field 1.5 m away from a positive charge of 2.1*10^-9 C?

(e.g. 1.0 N/C)

(e.g. "outward" or "inward")

Section 3. Gravitational Potential vs. Electric Potential

Any matter lifted from the surface of the earth has a potential energy. This gravitational potential energy is given by the formula PE=mgh, and the potential energy can be altered by changing its height. The electrical potential energy also can be changed by changing distance between two charges.

Gravitational potential energy equals to product of the mass of an object, gravitational field force, and its height from the earth.

PE_G = mgh

where:

m is the mass of the ball (kg),
g is the gravitational field force (g = 9.8 m/s²), and
h is the distance between the ball and the earth (m).

Electric potential energy equals to the electric potential energy divided by charge.

PE = qEd (see right)

where:

q is the charge of an object (C),
E is electric field produced by Q (N/C), and
d is the distance between the two charges. (see right)

Electric potential is called Voltage, which can be derived from above equation.

Voltage is also related to force.

V = Ed = (F/q)*d = Fd/q= W/q

(W = Fd -- force times displacement in the direction of force is work (J))

A high voltage means that each individual charge is experiencing a large force. A low voltage means that each individual charge is experiencing a small force.


	"q" on A has smaller force than "q" on B. If the distance of B is one half of that of A, the force acting on B is twice as large as A because the force is inversely proportional to the square of the distance between two charges.

Example problem 2.

From the diagram of A and B above, r_A is 0.0005 m and r_B is 0.0003 m. What is the force acting on q at A and B, if the charge of q is 1.2 * 10^-11 C and the charge of Q is 1.5 * 10^-11 C?

(e.g. 1.00*10^-10 N) A =

(e.g. 1.00*10^-10 N) B =

A has high potential energy because these particles want to separate from each other.

B has high potential energy because these particles want to come together. It is the same priciple as the gravity.

C has lower potential energy compared to A because the electric field force is inversely proportional to the square of its distance.

D has lower potential energy compare to B for the same reason.

When same charges are put close together, we say we have a high voltage because it has a high potential energy.

Largeer the distance is, the smaller the force and voltage are.

	If the spheres are broght close together, the charge will try to get as far away from each other as possible. As a result, the voltage becomes equal on both sphere.

Charge will always move until the force acting on it is reduced to a minimum or until the voltage becomes the same.

Section 4: Chapter Quiz

Try Chapter 12 Quiz and see how much you learned.

[Ch 11] - [Ch 12] - [Ch 13] - [Ch 14] - [Ch 15]