## Sunday, 5 June 2011

### Gravitational Potential vs. Electric Potential

Gravitational Potential vs. Electric Potential
 Any matter lifted from the surface of the earth has a potential energy. Thisis given by the formula PE=mgh, and the potential energy can be altered by changing its height. The  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.PEG = 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.

### Gravitational Field vs. Electric Field

• Gravitational Field vs. Electric Field
 Let us have your opinion about the attraction of an object. The concept of  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 of the earth, i.e., the gravity (g = 9.8 m/s2), but where does this number come from? It comes from Newton's . 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), me = mass of the earth (kg), mo = 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 "me" is the mass of the earth and "d" is its radius (we are talking about gravitational force on the surface of the earth.).

The (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 sic. ymetrField 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.
vitational Field vs. Electric Field

# Electric and Magnetic Constants

In the equations describing electric and magnetic fields and their propagation, three constants are normally used. One is the speed of light c, and the other two are the electric permittivity of free space ε0 and the magnetic permeability of free space, μ0. The magnetic permeability of free space is taken to have the exact value

This contains the force unit N for Newton and the unit A is the Ampere, the unit of electric current. With the magnetic permeability established, the electric permittivity takes the value given by the relationship

where the speed of light c is given by
This gives a value of free space permittivity

which in practice is often used in the form
These expressions contain the units F for Farad, the unit of capacitance, and C for Coulomb, the unit of electric charge.
In the presence of polarizable or magnetic media, the effective constants will have different values. In the case of a polarizable medium, called a dielectric, the comparison is stated as a relative permittivity or a dielectric constant. In the case of magnetic media, the relative permeability may be stated.

### The Electric Drift Field for the STAR TPC

The Electric Drift Field for the STAR TPC   When a charged particle traverses the TPC volume, it ionizes gas atoms every few tenths of a millimeter along its path and leaves behind a cluster of electrons.  The electron clusters then drift to the anode plane under the influence of an externally applied electric field where their time of arrival and location is recorded.
An animated simulation of the drift is available here.

In the STAR TPC, the electric field is provided by the outer field cage (OFC), the inner field cage (IFC), and the high voltage central membrane (CM).  The purpose of the OFC and IFC is to provide a nearly perfect electric field in which to drift the electrons to the anode plane since any distortions in the field will result in a distortion of the recorded tracks.  The OFC and the IFC also serve to define the active gas volume and were designed to contain the TPC gas and prevent it from being contaminated with outside air.  The central membrane is located in the middle of the TPC and is held at high voltage.  The anode and pad planes are organized into sectors on each end of the TPC and the pads are held at ground potential.   The OFC and IFC include a series of gradient rings that divide the space between the central membrane and the anode planes.  The total distance from the CM to either anode plane is slightly greater than 2 meters. There is approximately one ring per centimeter and the rings are biased by a chain of resistors that connect to the CM, the anode plane ground, and each of the gradient rings inbetween.  The rings are separated by two-megohm resistors and there are 182 rings and 183 resistors in each chain.

The last two resistors are adjustable and are housed in a rack which is external to the TPC.  Note that the outer field cage has a "ground shield" attached to ring 182.  It marks the end of the TPC drift volume and is used to better define the shape of the field at the terminus.   The inner field cage does not have a "ground shield".   The spark gaps are safety devices for the protection of personnel and equipment in case the external resistors are disconnected while the field cages are biased.
There are four resistor chains.  One for each end of the two field cages.  Thus, IFC East, IFC West, OFC East, and OFC West.

# THE ELECTRIC FIELD

## Introduction

The presence of an electric charge produces a force on all other charges present. The electric force produces action-at-a-distance; the charged objects can influence each other without touching. Suppose two charges, q1 and q2, are initially at rest. Coulomb's law allows us to calculate the force exerted by charge q2 on charge q1 (see Figure 23.1). At a certain moment charge q2 is moved closer to charge q1. As a result we expect an increase of the force exerted by q2 on q1. However, this change can not occur instantaneous (no signal can propagate faster than the speed of light). The charges exert a force on one another by means of disturbances that they generate in the space surrounding them. These disturbances are called electric fields. Each electrically charged object generates an electric field which permeates the space around it, and exerts pushes or pulls whenever it comes in contact with other charged objects. The electric field E generated by a set of charges can be measured by putting a point charge q at a given position. The test charge will feel an electric force F. The electric field at the location of the point charge is defined as the force F divided by the charge q:

Figure 23.1. Electric force between two electric charges.

The definition of the electric field shows that the electric field is a vector field: the electric field at each point has a magnitude and a direction. The direction of the electric field is the direction in which a positive charge placed at that position will move. In this chapter the calculation of the electric field generated by various charge distributions will be discussed.