3. Voltage Voltage is electric potential energy per unit charge, measured in joules per coulomb ( = volts). It is often referred to as "electric potential", which then must be distinguished from electric potential energy by noting that the "potential" is a "per-unit-charge" quantity. Like mechanical potential energy, the zero of potential can be chosen at any point, so the difference in voltage is the quantity which is physically meaningful. The difference in voltage measured when moving from point A to point B is equal to the work which would have to be done, per unit charge, against the electric field to move the charge from A to B.electric potential energycharge mechanical potential energyzero of potentialworkelectric field

8. Work and Voltage: Constant Electric Field The case of a constant electric field, as between charged parallel plate conductors, is a good example of the relationship between work and voltage.electric fieldwork voltage The electric field is by definition the force per unit charge, so that multiplying the field times the plate separation gives the work per unit charge, which is by definition the change in voltage.

9. This association is the reminder of many often-used relationships: Voltage Difference and Electric Field The change in voltage is defined as the work done per unit charge against the electric field. In the case of constant electric fieldwhen the movement is directly against the field, this can be writtenvoltageworkelectric fieldconstant electric field

10. If the distance moved, d, is not in the direction of the electric field, the work expression involves the scalar product:scalar product In the more general case where the electric field and angle can be changing, the expression must be generalized to a line integral:general caseline integral

11. Voltage from Electric Field The change in voltage is defined as the work done per unit charge, so it can be in general calculated from the electric field by calculating the work done against the electric field. The work per unit charge done by the electric field along an infinitesmal path length ds is given by the scalar productvoltageworkelectric fieldinfinitesmalscalar product

12. Generator Van de Graaff VoltagesVoltages of hundreds of thousands of volts can be generated with a demonstration model Van de Graaff generator. Though startling, discharges from the Van de Graaff do not represent a serious shock hazard since the currents attainable are so small.shock hazard A pulley drives an insulating belt by a sharply pointed metal comb which has been given a positive charge by a power supply. Electrons are removed from the belt, leaving it positively charged. A similar comb at the top allows the net positive charge* to spread to the dome.

13. A favorite demonstration with the Van de Graaf is to make someone's hair stand on end.

14. *electrons are of course the mobile charge carriers. Experimenters Erin Klein Jacobs above and Nehlia Grey at right demonstrate the reality that like charges repel. The strands of their hair all have the same net charge and therefore repel each other strongly.

15. The potential (voltage) of a point charge can be evaluated by calculating the work necessary to bring a test charge q in from an infinite distance to some distance r. The zero of potential is chosen at infinity.voltagepoint chargezero of potential Considering a radial path from a to b, the work done by the Coulomb force is obtained from a line integral which in this case becomes just a polynomial integral since we are moving along a straight radial line:workCoulomb forceline integralpolynomial integral

18. Multiple Point Charges The electric potential (voltage) at any point in space produced by any number of point charges can be calculated from the point charge expression by simple addition since voltage is a scalar quantity. The potential from a continuous charge distribution can be obtained by summing the contributions from each point in the source charge.voltagepoint charge expression continuous charge distribution The calculation of potential is inherently simpler than the vector sum required to calculate the electric field.electric field

21. Multiple Point Charges The electric field from multiple point charges can be obtained by taking the vector sum of the electric fields of the individual charges.electric fieldpoint chargesvector sum

22. After calculating the individual point charge fields, their components must be found and added to form the components of the resultant field.point charge fieldscomponents The resultant electric field can then be put into polar form. Care must be taken to establish the correct quadrant for the angle because of ambiguities in the arctangentpolar formambiguities in the arctangent The electric field from multiple point charges can be obtained by taking the vector sum of the electric fields of the individual charges.electric fieldpoint chargesvector sum

23. The continuous charge distribution requires an infinite number of charge elements to characterize it, and the required infinite sum is exactly what an integral does. To actually carry out the integration, the charge element is expressed in terms of the geometry of the distribution with the use of some charge density. Continuous Charge Distributions The electric potential (voltage) at any point in space produced by a continuous charge distribution can be calculated from the point charge expression by integration since voltage is a scalar quantity.voltagepoint charge expression

25. One of the values of calculating the scalar electric potential (voltage) is that the electric field can be calculated from it. The component of electric field in any direction is the negative of rate of change of the potential in that direction.voltageelectric field If the differential voltage change is calculated along a direction ds, then it is seen to be equal to the electric field component in that direction times the distance ds.differential The electric field can then be expressed as This is called a partial derivative.partial derivative Electric Field from Voltage

26. Electric Field as Gradient The expression of electric field in terms of voltage can be expressed in the vector formelectric field in terms of voltage This collection of partial derivatives is called the gradient, and is representedpartial derivativesgradient by the symbol.. The electric field can then be written For rectangular coordinates, the components of the electric field are

27. Obtaining the value of the Electrical Field From the Electrical Potential E ds dV = 0

35. T U G A S Buat makalah tentang aplikasi elektrostatis