A small nonconducting ball of mass m=1.0mg and charge q=2x10^-8C(distributed uniformly through its volume) hangs from an insulating thread that makes an angle of 30 degrees with a vertical, uniformly charged nonconducting sheet. Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density of the sheet?

Lets name the angle of the thread with the vertical: a = pi/6 (30 degrees) and the surface density of electric charge on the sheet be b (measured in C/m^2)

The forces acting on the ball are:
The vertical force of gravitation:
F_g = mg
And the horizontal electric ...

The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. Thank you.
Start with P0 = 0 and use Jacobi iteration to find.....
(Complete problem found in attachment)

Dry air will break down and generate a spark if the electric field exceeds about 2.95 x 10^6 N/C. How much charge could be packed onto a green pea (diameter 0.830cm) before the pea spontaneously discharges?

A particular diet calls for exactly 1000 units of vitamin A, exactly 1600 units of vitamin C, and exactly 2400 units of vitamin E. An individual is fed a mixture of three foods. Each gram of food 1 contains 2 units of vitamin A, 3 units of vitamin C, and 5 units of vitamin E. Each gram of food 2 contains 4 units of vitamin A, 7

See attached file for the graph.
Three infinite planes of surface charge densities of ?
s = 2, -3, and 0.5
¼C/m2 lies parallel the xy plane as shown in Figure 1, each separated by
a 1 mm air gap.
Find the field at:
i. z = 0.2mm
ii. z = 1.2 mm
iii. z = 2.2mm
iv. z = -2.2mm

(a) Consider a vector function with the properly ... = 0 everywhere on two closed surfaces S1 und S2 and in the volume V enclosed by them (see the figure). Show that the flux ol F through S1, equals the flux of F through S2. In calculating the fluxes, choose the direction of the normals as indicated by the arrows in the figure.

1. Find the sum of the first five terms of the geometric sequence.
A=3, r=2
2
a. 93 b. 5 c. 1 d. 93
2 2
2. Use the Gauss-Jordan method to solve the system of equations.
x - y + 3z = 16
3x + z = 4
x + 2y + z = -4
a. No solution b. (4, 0, -4)

I would like a short explanation of Gaussian Elimination with partial pivoting and Gauss-Seidel. Also, explain when each applies or when one is better than the other. Please include some examples.