Equipotentials and Lines of Force
The electric field lines of force are to be mapped for various configurations of electrodes. However, because direct mapping of the electric field lines cannot be accomplished, the surfaces on which the voltage is constant (equipotentials) will first be determined. The relationship between equipotentials and electric fields will then be utilized in order to draw the lines of force.
When charges are moved to fixed position in space, the region in the vicinity of the charges is altered and it is said that the chases have set up an electric field. In order to measure the strength and direction of the electric field, a positive test charge, qo, is placed in the field and the resulting force on the test charge is measured. The electric field strength is then
The limit is taken to indicate that the test charge must be small enough so that it does not affect the original charge distribution that set up the field. Notice that the direction of the field is the same as the direction of the force on the positive test charge.
The electric field lines of force are not measured directly. The equipotentials are first determined, then the relationship between electric fields and equipotential surfaces us used to find the electric field lines of force; that is,
[pic] (1) or, [pic] (2)
where V is the electric potential. These equations indicate that the lines of force of the electric
Fields are perpendicular to the equipotentials.
The equipotentials are surfaces on which no work is done when a charge is moved along the surface from one point to other. A characteristic associated with the surface is that the voltage is the same everywhere on the surface. Because voltages can be measured easily, this allows the equipotential surfaces to be mapped. Once they are determined, the electric field lines of force can be drawn by noting from (1) or (2) that the field and equipotential surfaces are mutually perpendicular.
o equipotential and field mapper with leads 3 sheets of conductive paper with different electrode designs metal pushpins o DC power supply (Tri-Power Supply) with leads o VOM with leads o 3 sheets of centimeter graph paper
1) Use four pushpins to attach the sheet of the conductive paper with point electrodes to the corkboard.
2) Connect the DC power supply and the VOM as shown in Figure 1.
Figure 1. The arrangement of the equipment.
3) Turn on the DC power supply and the VOM. Set the VOM to read 20 volts. Touch the positive electrode on the equipotential and field mapper with the moveable electrode, and adjust the DC power supply until the voltage reading on the VOM is 8.00 volts.
4) Move the moveable electrode to a position on the conductive sheet until the reading on the VOM is 7 volts. Record this position on your graph paper. Locate a second position and record. Continue in this fashion until enough points have been recorded to allow a smooth curve to be drawn through the points. (If the 7-volt equipotential is located too close to the fixed electrode to make an accurate determination of its position, then start with the 6 volt equipotential.)
5) Repeat step (4) for 6, 5, 4, 3, 2, and 1-volt equipotentials. (If the I volt equipotential is too close to the electrode for an accurate determination, then ignore it.)