The electric field of infinite line charges and infinite sheet of charges

[dada130500015]

Homework Statement

Q1,Infinite uniform line charges of 5 nC/m lie along the x and y axes in free space. Find E at (a), P(0, 0 , 4); and (b), P (0 ,3 , 4)


Q2, Three infinite uniform sheets of charge are located in free space as follows: 3 nC/m² at z= -4, 6 nC/m² at z=1, -8 nC/m² at z=4. Find E at point P (2,5,-5)

Homework Equations

E=ρ_L/2∏ε0ρ
Q1,I used this got: a), E=22.5z V/m
b), E=10.8y + 14.4z V/m
Q2, I used E= ρ/2ε0

The Attempt at a Solution

Q1, The right answer is a), E=45z V/m b), E = 10.8y+36.9z V/m


I really confused in this topic, So wish your guys help me. Thanks a lot.

 

[WJSwanson]

Is the $\rho$ in the denominator of your E_line function supposed to be the density? Or is it the displacement from the line of charge? Also, it would be helpful if you could show your calculations step-by-step because I get the correct answer for (a) using

$E = \frac{\lambda}{2\pi\epsilon_{0}r}$

as you had there, combined with the superposition principle. And I got the correct answer for (b) using the superposition principle and the same function you listed of

$E = \frac{\sigma}{2\epsilon_{0}}$

So I don't know if you just aren't superposing the charge distributions' respective fields properly or if you made some incorrect substitutions. So post your calculations step-by-step so we can actually see where you might be going wrong.

 

[dada130500015]

In Q1, the ρ is the density i think.
Here is the step for Q1:
a), E=ρL/2∏ε0ρ
= (5*10^-9/2*∏*ε₀*4²)*4z
=22.5z V/m

b), E={5*10^-9/2*∏*ε₀*(3²+4²)}*(3y+4z)
=10.8y + 14.4z V/m


For Q2, i still can't got the answer that using the E=σ/2ϵ₀,
in this question i just calculate each of three with the formula above and then add them to find the E. could you show me the step?

 

[dada130500015]

is the $\rho$ in the denominator of your e_line function supposed to be the density? Or is it the displacement from the line of charge? Also, it would be helpful if you could show your calculations step-by-step because i get the correct answer for (a) using

$e = \frac{\lambda}{2\pi\epsilon_{0}r}$

as you had there, combined with the superposition principle. And i got the correct answer for (b) using the superposition principle and the same function you listed of

$e = \frac{\sigma}{2\epsilon_{0}}$

so i don't know if you just aren't superposing the charge distributions' respective fields properly or if you made some incorrect substitutions. So post your calculations step-by-step so we can actually see where you might be going wrong.

In Q1, the ρ is the density i think.
Here is the step for Q1:
a), E=ρL/2∏ε0ρ
= (5*10-9/2*∏*ε0*42)*4z
=22.5z V/m

b), E={5*10-9/2*∏*ε0*(32+42)}*(3y+4z)
=10.8y + 14.4z V/m


For Q2, i still can't got the answer that using the E=σ/2ϵ0,
in this question i just calculate each of three with the formula above and then add them to find the E. could you show me the step?