Electric Fields Experiment Physics 222 Lab Instructor: Saban Hus Jock Lillard January 21, 2009 Theory: An electrical field is defined as a space in which if there is a small positive test charge, there will be a force exerted on said charge. The magnitude of the field is defined by the force divided by the magnitude of the charge, or E=F/q (1). If the charge distributions are known, Coulomb’s law can be used to calculate the electrical field, but these distributions are hard to locate. Luckily, the field can be measured by other indirect means such as measuring the electric potential and using the relationships between the electric potential and electric field strength. A potential difference exists in a field when work is required to move a charge between two points in that field, and it is defined by the work required divided by the test charge, or V=W/q (2). The simple work equation states that work is equal to a force times the distance over which that force was exerted. Therefore a relationship between V and E can be defined as V=(Fd)/q (3). Then substituting in equation (1) into equation (3), V=(qEd)/q (4), or V=Ed (5). If the electric field is not uniform at different points in space, then the electric field strength is found by E=ΔV/Δd (6). Therefore, the electric field at any point may be found by measuring the potential difference between two nearby points and dividing by the distance between these two points. Method: A glass tray is filled with an ionic solution and is used to map out two electric fields and their strengths at different points. Two conducting electrodes are placed ten centimeters apart and a source of emf is applied to them. The electric field strength is first measured by using a digital voltmeter and mapped out on graph paper for every volt from 1 to 9. Two different fields were created. The first used two metal bars that spanned the length of the glass as the electrodes, and the second field used only two small vertical rods as the electrodes. Two random points were found in both fields that were used to calculate the electrical field strength. Results: (See attached). At each random point, secondary points, one .5 cm in front and one .5 cm behind, were marked. These points ran perpendicular to the equipotential lines and therefore mark the point at which potential change is the greatest. Equation (6) was then used to determine the potential difference. The potential difference in the field containing the bar electrodes showed to be 90 at point A and 80 at point B. The second field had potential differences of 50 at point A and 30 at point B. Error Analysis: The high difference in the potential differences is easily explainable. The first source of error came as the electrical field was mapped out on graph paper. The equipotential lines were roughly sketched, and therefore were slightly flawed. This caused the second source of error—the secondary points were not exactly perpendicular, therefore the maximum potential difference was not always obtained. The final source of error resulted from an inaccurate measurement of .5 cm in front and behind the random point. Other minor errors could have occurred from inaccurate readings, but the other three explanations are far more likely to cause the differences in measurement. Questions: (See Attached)