A charge q= 2.00 μC is placed at the origin in a region where there is already a uniform electric field = (100 N/C) . Calculate the flux of the net electric field through a Gaussian sphere of radiuscentered at the origin. (ε0= 8.85 × 10-12C2/N. m^2)

a. 2.26 × 10^5 N · m^2/C

b. 5.52 × 10^5 N · m^2/C

c. 1.13 × 105 N · m^2/C

d. zero

A.

Explanation:

The flux through the  Gaussian  sphere of radius centered at the origin,

Therefore:

φ

charge:  

,

φ=

substitute the values

φ=

φ=

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14

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