User:Shahsaurabh02/sandbox

'Electric Field Intensity'

An electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the surrounding force of an electrically charged particle exerted on other electrically charged objects. The concept of an electric field was introduced by Michael Faraday.

The superposition principle holds for an infinite number of infinitesimally small elements of charges – i.e. a continuous distribution of charge. The limit of the above sum is the integral:

where ρ is the charge density (the amount of charge per unit volume), and dV is the differential volume element. This integral is a volume integral over the region of the charge distribution.

The electric field at a point is equal to the negative gradient of the electric potential there, Coulomb's law is actually a special case of Gauss's Law, a more fundamental description of the relationship between the distribution of electric charge in space and the resulting electric field. While Columb's law (as given above) is only true for stationary point charges, Gauss's law is true for all charges either in static or in motion. Gauss's law is one of Maxwell's equations governing electromagnetism. Gauss's law allows the E-field to be calculated in terms of a continuous distribution of charge density

where ∇⋅ is the divergence operator, ρ is the total charge density, including free and bound charge, in other words all the charge present in the system (per unit volume).

'Capacitor'

A capacitor (originally known as condenser) is a passive two-terminal electrical component used to store energy electrostatically in an electric field. By contrast, batteries store energy via chemical reactions. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric (insulator); for example, one common construction consists of metal foils separated by a thin layer of insulating film. Capacitors are widely used as parts of electrical circuits in many common electrical devices. When there is a potential difference (voltage) across the conductors, a static electric field develops across the dielectric, causing positive charge to collect on one plate and negative charge on the other plate. Energy is stored in the electrostatic field. An ideal capacitor is characterized by a single constant value, capacitance. This is the ratio of the electric charge on each conductor to the potential difference between them. The SI unit of capacitance is the farad, which is equal to one coulomb per volt. The capacitance is greatest when there is a narrow separation between large areas of conductor, hence capacitor conductors are often called plates, referring to an early means of construction. In practice, the dielectric between the plates passes a small amount of leakage current and also has an electric field strength limit, the breakdown voltage. The conductors and leads introduce an undesired inductance and resistance. Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In filter networks, they smooth the output of power supplies. In resonant circuits they tune radios to particular frequencies. In electric power transmission systems they stabilize voltage and power flow.

' Van-De-Graaff Generator' 1) hollow metal sphere 2) upper electrode 3) upper roller (for example an acrylic glass) 4) side of the belt with positive charges 5) opposite side of the belt with negative charges 6) lower roller (metal) 7) lower electrode (ground) 8) spherical device with negative charges, used to discharge the main sphere 9) spark produced by the difference of potentials

A simple Van de Graaff-generator consists of a belt of silk, or a similar flexible dielectric material, running over two metal pulleys, one of which is surrounded by a hollow metal sphere.[1] Two electrodes, (2) and (7), in the form of comb-shaped rows of sharp metal points, are positioned respectively near to the bottom of the lower pulley and inside the sphere, over the upper pulley. Comb (2) is connected to the sphere, and comb (7) to the ground. A high DC potential (with respect to earth) is applied to roller (3); a positive potential in this example. As the belt passes in front of the lower comb, it receives negative charge that escapes from its points due to the influence of the electric field around the lower pulley, which ionizes the air at the points. As the belt touches the upper roller (6), it transfers some electrons, leaving the roller with a negative charge (if it is insulated from the terminal), which added to the negative charge in the belt generates enough electric field to ionize the air at the points of the upper comb. Electrons then leak from the belt to the upper comb and to the terminal, leaving the belt positively charged as it returns down and the terminal negatively charged. The sphere shields the upper roller and comb from the electric field generated by charges that accumulate at the outer surface of it, causing the discharge and change of polarity of the belt at the upper roller to occur practically as if the terminal were grounded. As the belt continues to move, a constant charging current travels via the belt, and the sphere continues to accumulate negative charge until the rate that charge is being lost (through leakage and corona discharges) equals the charging current. The larger the sphere and the farther it is from ground, the higher will be its final potential. Another method for building Van de Graaff generators is to use the triboelectric effect. The friction between the belt and the rollers, one of them now made of insulating material, or both made with insulating materials at different positions on the triboelectric scale, one above and other below the material of the belt, charges the rollers with opposite polarities. The strong e-field from the rollers then induces a corona discharge at the tips of the pointed comb electrodes. The electrodes then "spray" a charge onto the belt which is opposite in polarity to the charge on the rollers. The remaining operation is otherwise the same as the voltage-injecting version above. This type of generator is easier to build for science fair or homemade projects, since it doesn't require a potentially dangerous high voltage source. The trade-off is that it cannot build up as high a voltage as the other type, that cannot also be easily regulated, and operation may become difficult under humid conditions (which can severely reduce triboelectric effects). Finally, since the position of the rollers can be reversed, the accumulated charge on the hollow metal sphere can either be positive or negative. A Van de Graaff generator terminal doesn't need to be sphere shaped in order to work, and in fact the optimum shape is a sphere with an inward curve around the hole where the belt enters. Since electrically charged conductors have no e-field inside, charges can be added continuously. A rounded terminal minimizes the electric field around it, allowing greater potentials to be achieved without ionization of the surrounding air, or other dielectric gas. Outside the sphere the e-field quickly becomes very strong and applying charges from the outside would soon be prevented by the field. Since a Van de Graaff generator can supply the same small current at almost any level of electrical potential, it is an example of a nearly ideal current source. The maximum achievable potential is approximately equal to the sphere's radius multiplied by the e-field where corona discharges begin to form within the surrounding gas. For example, a polished spherical electrode 30 cm in diameter immersed in air at STP (which has a breakdown voltage of about 30 kV/cm) could be expected to develop a maximum voltage of about 450 kV.