Calculating Electric Field and Flux Density - Point Charges Homework Solution

[batman2020]

Homework Statement

Point charges of 12x10-6, -7x10-6 and 4x10-6 are located at (2,0,-1), (1,1,2) and (2,-1,2).

a. Determine D(flux density) and E(electric field strength) at (1, -1, 3).

b. What is the flux passing through the sphere of radius of 2.5 centered on the origin

Homework Equations

E=The sum of[(Q/4(pi)(epsilson))x(the unit vector between E and the point)]

D=The sum of[(Q/4(pi)(r^2))x(the unit vector between D and the point)]

The Attempt at a Solution

a. I found the electric field due to each point at (1, -1, 3) and I got the answer of
E=11.9x103ax+19.17x103ay+29.35x103az N/C


I did the same with D except multiplied across by epsilon and divided by r^2 and I got
D=(0.105x10-6ax+0.168x10-6ay+0.2599x10-6az)/r^2

b. I just substituted r into the answer I got for D and got
D=1.68x10-8ax+2.688x10-8ay+4.1584x10-8az

I was just wondering if somebody could confirm if these answers are right or wrong

 

[KataKoniK]

.

Thank you for your post. Your calculations for part a seem to be correct, as they align with the given point charges and their locations. However, I would suggest double-checking your calculations for part b. The flux passing through a sphere of radius 2.5 centered at the origin can be found using the equation:

Φ = ∫∫∫ D · dA

Where D is the electric flux density and dA is the differential area element. You can use the formula you provided for D in your solution and integrate over the surface of the sphere to find the total flux passing through it. I hope this helps. Keep up the good work!