Components in Electricity

Understanding charges in 2-D:

We have learned a lot about voltage in the past. Voltage is electric force multiplied by distance, which is also k multiplied by charge and divided by radius squared when the charge is in a straight line. Today, we are learning about the charges when it has a component on it. To find the radius, we can use pythagorean theorem. The equation of this radius can be substituted into the equation of the voltage when the radius is unknown. First, we are integrating in respect to r, then we found the equation to be k multiplied by charge divided by the radius. The radius is substituted with the sqrt(x(square) + a(square). From that, we find the equation as below.

The electric force itself can have component.

We are now given a ring with 20 point charges acring on a single point. The point is at a distance 20cm away from the center of the ring, and the radius of ring is 30 cm. We can calculate this by hand, which will be using equation of voltage as kq/sqrt(radius(square)+x(square)). By plugging in the known, we find the voltage to be 4.99x 10(5) as below.

We can also use spreadsheet to calculate the total voltage. We set the known in for radius, x, charge, and constant as below. Then we set the equation to be ... For 20 points. Then we add all of the voltages and found the answer to be the same as done by hand.

In the spreadsheet, we recorded the x and y-axis. Y is the same for every point of x, but x changes every 0.01 since we will split it up into 16 parts. K is always the same and charge is also given. We wanna calculate r first which equation would be ... And also set equation of voltage to be. Finally, we will sum all the voltages to find the V total as below.

A rod with length of 0.16m with charges that is located at (0.1,0.15) is given. We want to find the total voltage at the rod. If we split the rod into 16 parts, doing the calculation by hand would be tidious; thus, we use spreadsheet to calculate them.

We also find the relationship between k, lamda, q, a, x, and b. We know that the volte is integration of k