4/16 week 8 day 2 Potential-of-Continuous-Charge-Distributions

The first thing we do today is that find the electric potential energy. In the photo, there is a ring with charge, and we should find one point's electric potential energy of the charge in the top of the ring. And we use the equation V=kq/r, and r =sqar(x^2+a^2)

in this photo, we find another  point's potential energy of different charge in the ring. one is in the top and another is at the middle of ring's one side. and we ues the same equation  V=kq/r, but the r is different, one is sqar(x^2+4a^2),another is sqar(2a^2+x^2)

in this photo, we find  the angle's relationship with a and x, and find three equations of theta.

in this photo, we change V=kq/r to V(theta)=kqcos(theta)/x

in this photo, we use the excle to find the total potential energy of the ring, the ring divided into 16 parts, and one part's potential energy is V=kq/r, the total potential energy is that add all parts together.

in this photo, we calculate the total electric potential energy  of the ring and find it is same in the excle we did.

in this photo, we use the potential energy V to find the electric field E, we put the equation cos(theta)=x/sqar(x^2+a^2) and r=sqar(a^2+x^2) to E=kQcos(theta)/r^2, and we find that E=kQx/(x^2+a^2)^(3/2).

in this photo, we use the antiderivative to find the change of the potential energy V, we use the equation E=kQx/(x^2+a^2)^(3/2), and find out that V=kQ/sqar(x^2+a^2) from infinite to x.

in this photo, we should calculate the potential electric energy of a special point.

in this photo, we use the equation at the bottom of the graph to find the potential electric energy.

in this photo, we use the excle to find the answer and find it is same as what we did in the last photo.

in this photo, there is a particl has positive charge, and we draw the points which have the same potential electric energy and line them, we fing these particals can make different circle.

in this photo, we have two different lines, one has positive charge, another has negative charge. and we draw  the surface that has same potential electric energy.

in this photo, we have a couple of dipole that draw the surface that has same potential electric energy.

Electric Potential Lab/Activity

 
Pictured above are the various pieces of equipment used to run this activity. We had a power source connected to two points on the conductive paper, which we then turned on to run a voltage through. We then used a voltmeter to measure the magnitude of the voltage at various distances. This was done by placing both of the voltmeter needles are precise lengths from each other. The Position values shown below depict the distance and direction that one of the needles moved in relation to the other stationary needle, which was left at the origin (one of the metal circles on the paper). 

then we start to do another experiment in the photo.we use cork board, conductive paper,power supple,voltmeter to find at the different distant, what is the voltage between the two metallic paint marks on the paper.

in this photo, we use the excle to find the at the different position what is the voltage and the change of V/x

Conlcusion:

Today in class, we build three different methods of finding potential difference V between two points. And we 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 by using a spreadsheet, algebraically/trigonometrically by solving for V, and solving for V using Gauss' Law. 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. It allowed us to gather some data and calculate how much work a charge would have to do to move from one point on the paper to another using the equation W=QdV.