Potential, Charge distributions

Lab Day 14 :4/16 Potential, Charge distributions

Purpose: The purpose is to explore the potentials on different types of charge distributions: on a ring of charge or a charged rod at a given point. The different methods of deriving the calculations of cell potential at a point will be identified and compared using excel and manual calculations.

Calculations:

Potential from a Charged Ring

We came up with the calculations of the potential from a charged ring in that we found the exact value through the integral. The integral was used where all the charges in a ring of charge q is the same distance r from point P on the ring of the axis which therefore makes r constant. The limits of integration was from 0 to 20. The value obtained was then compared to the excel calculations where we divided the ring into 20 segments which gave an approximation of the total potential.

Change in potential using E-Field

Another method we can use to calculate cell potential in the same problem is taking the integral of the E-field. In the calculations, we were able to find the E-field in the x-component as the y-component cancels out. Next, the potential was found using the integral of the Electric field in the x-component and setting the limits of integration from infinity to x.  

The equation calculated symbolically came out to be the same as the first method. 

Potential of Finite length Line Charge

Looking at a finite-length line-charge, we found the electric potential using the the given charge density and adding up all the infinitesimal point charges using the integral of potential. Therefore the potential at the desired point can be found using the symbolic solution. In fact if we wanted to find the work done to move a charge from one point to another then we can use W=QdeltaV. We can observe that the work done is independent the path along which the charge 
moves. Therefore if we move the charges, the work will not change. 

Equipotentials

The idea of an equipotential surface is that no work is done when the electric charge travels along that surface. Therefore making equipotential lines always perpendicular to the electric field lines.The potential is the same at every point of the surface. 

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Experiment: Electric Potential Lab/Activity

In this experiment, we measured the electric potential at several points on a sheet due to a potential difference. The setup below shows a conductive paper with two point charges attached to a power supply creating a potential difference of the voltage source. We moved the voltmeter 1 cm intervals toward the right creating 10 points and also measured the in between points. The main conclusions of this activity is that the ratio of the (change in voltage and change of position) is the same as the electric field strength. The potential energy goes from high to low in the direction of the electric field as seen in our results below.

Potential vs. Position Graph of Results

Conclusion: We can calculate the potential from a charged ring using the limit of the sum as an integral and also using the integral of the Electric field as both gives the same results. We also explored the idea of a Finite line of charge where the electric potential was once again calculated and approximated using excel. The idea of equipotential surface is important for analyzing potentials on a surface as the potentials are the same at every point on the surface in which it is perpendicular to the electric field. Based on our experiment, we also found that he potential decreases toward the direction of the electric field strength.