CAPACITOR

CAPACITOR

Figure 1: Examples of capacitor

Capacitor is a device that stores electric potential energy by storing separated positive and negative charges.

Figure 2: Visual of two charged plate

Work done to separate the positive charge from negative charge since there is an attractive force between the two charges. The work done to separate the charges is called electric potential energy.

An electric field lines arises between the two conductors. The field lines beginning on the conductor with positive charges and ending on the conductor with negative charge.

Electric potential energy is the energy stored in an electric field.

A parallel plate capacitor is one of the simplest form of capacitor. It consisting of two metal plates each of the same area, A and separated by distance, d. A charge +Q are on one plate and another charge -Q on the other. (Assume that the plates are separated by air gap.

If charge magnitude Q us evenly spread over each plate with surface area A, then the surface charge density is denoted by

The magnitude of the electric field outside the conductor is

With

Since the field between the plates is uniform, the magnitude of the potential difference is

The constant of proportionality between charge and potential difference depends only on geometric factors, size and shapes of the plates and also the material between the plates.

Where

     Q  is the magnitude of the charge on each plate

   is the magnitude of the potential difference between the plates

     C  is the constant proportionality or capacitance

CAPACITANCE, C can be thought as the capacity to hold charge, Q for a given potential difference .

The SI unite of capacitance are Coulombs per volts, C/V (which is called farad, F)

(commonly microfarads, nano-farads, or picofarads)

To find capacitance for parallel plate capacitor, the electric field is

Where A is the inner surface area of each plate. If the distance of each plate is d, then the magnitude of the potential difference is

Q can be written as:

Thus capacitance of a parallel plate capacitor is

A large charge is important to store in a capacitor. In order, to store the charge without making the potential difference between the plate excessively large, we need large capacitance.

• Capacitance ix inversely proportional to the spacing d between the plates, the air between the capacitor is not appropriate.
• Air can easily breakdown when the plate spacing is small
• Breakdown allows the spark to jump across the gap causing the stored charge lost.

One way to overcome this problem is to put insulator between the plates. Some insulating material also called dielectrics, can with stand electric field larger than those that cause air to breakdown. In addition the capacitance is also increase by placing the dielectrics between the plates.

For a parallel plate capacitor with dielectric fills between the plates , the capacitance is

K is the dielectric constant, it is the effect of the dielectric which increase the capacitance by a factor K.(K= 1, Air is slight larger than 1)

Dielectric constant determines how much charge can be stored for a given potential difference.

Dielectric strength determines how large a potential difference,  can be applied to a capacitor before dielectric breakdown occurs

POLARIZATION IN A DIELECTRIC

Polarization is a separation of the charge in an atom or molecule. There is two type which in polarized and unpolarized atom. The unpolarized atom with a central positive charge is surrounded by a cloud of electrons. When a positively charged, rod is brought near the atom, it repels the positive charge and attracts the negative charge in the atom.

Throughout the dielectrics, there a still equal amount of positive and negative charges. The net effect of polarization of the dielectric is a layer of positive charge on one side and negative side on another. The dielectric constant of a material is a measure of the ease it can be polarized. A larger dielectric constant indicates a more easily polarized material.

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ELECTRIC POTENTIAL

ELECTRIC POTENTIAL

Electric potential energy is the energy stored in an electric field. The change in potential energy when objects move around is equal in magnitude but opposite in sign to the work done by the field.

The electric force and electric potential energy for a pair of point of particles are proportional to the product of the charges of the particle

Figure 1: Electric Potential Energy

The charge of particles moves causing the electric potential energy changes. Just like mass in a gravitational field has gravitational potential energy, charges in an electric field have an electric potential energy. A charge’s electric potential energy store amount of energy it has. When set into motion by an electrostatic force, that energy can become kinetic and the charge can do work.

If the:

Two charges have opposite sign:

•                 Attract each other
•                Potential energy should be negative as the    is negative

Figure 2: Opposite Charges Attract

If the:

Two charges have same signs (either both positives or both negatives):

• ·         Repel each other

·         Potential energy should be positive as the    is positive

     

Figure 3: Same Charge Repel

ELECTRIC POTENTIAL DIFFERENCE

Potential differences are the changes in electric potential energy per unit charges

The electric force on charge is always directed toward regions of lower electric potential energy. For a positive charge, lower potential energy means lower energy but for a negative charge, lower potential energy means higher potential. This is because the force on a negative charge is opposite to the direction of E while the force on a positive charge is in the direction of E.

The magnitude of electric potential energy, V is

The unit of electric potential difference is or volts (V)

When a point charge, q moves from point A to point B, it moves through a potential difference

Video 1: Electric Potential Energy

EQUI-POTENTIAL SURFACES

All point on a equi-potential surface have the same electric potential. The electric potential V due to a point charge of +Q is 

The equi-potential surfaces are right angles to the electric field, E. No work is done in moving charge from one point to another point on the same equi-potential surface. For the same difference in electrical potential, the separation between equi-potential surfaces around a point charge increases as r increases.

Equi-potential surfaces and field lines are closely related. As long as the charge is moving in a direction perpendicular to the field, the work done by the field is zero and the potential stays the same. If you want to move a charge in a direction that maximizes the change in potential, you would move parallel or anti-parallel to the electric field.

The electric field is sometimes called the potential gradient.

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ELECTRIC FIELD

ELECTRIC FIELD 

Electric field, E, at a point can be defined as the electric force experienced by a test charge q at the point

Electric field can be defined as electric force per unit charge

A POINT OF CHARGE

The electric force on a charged body is exerted by the electric field, created by other charged body.

The charged body A produces or causes an electric field at point P. This electric field is present at P even if there is no charge at P; it is a consequence of the charge on body A only. Then a point charge q’ is placed at point P, it experiences the force F’. We can say that this force is exerted on q’ by the field at P

(Negative sign denotes that the direction of the electric field E is in the opposite direction of increasing r)

A charge particle moving through an electric field caused the electric potential energy changes.

• Two charges with opposite (Attract)

o   Potential energy (product of q1q2) should negative

• Two charges have same sign (Repel)

o   Potential energy (product of q1q2) should be positive

o   Electric force is repulsive

o   Potential energy increases as they move closer

Figure 1: Two different charge

ELECTRIC FIELD LINES

Electric field lines are an imaginary line or curve drawn through a region of space so that its tangent at any point is in the direction of the electric-field vector at that point (field lines are never intersecting)

Electric field lines show the direction of E at each point. The line spacing gives the magnitude of E at each point. When E is strong, the lines a drawn closely together while it far apart when it is weaker.

• Single positive charge – the line always points away from the charges and towards negatives charge
• Each point for opposite charge in space – the electric field vector is tangent to the field line passing through that line
• Each point for same charge in space – the lines are closer together where the field is strong, farther apart where it is weaker

Figure 2: Repulsion field lines (same charge)

Figure 3: Attraction field lines (opposite charge)

Figure 4: Single charge field lines (positive and negative)

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