Finding the E-field between two infinite plane charged sheets

In summary, we have two infinite-plane non-conducting sheets with surface charges of p1 = 13.35 uC/m2 and p2 = -8.65 uC/m2, parallel to each other with a distance of 0.245 m apart. The electric field between the sheets is calculated by summing the two charges over 2*epsilon_not, considering the negative direction of the field due to both sheets. The resulting answer is -1.2e6 N/C. However, the marking software may be sensitive to significant figures, so it is important to provide a more precise answer.
  • #1
aximwolf
14
0

Homework Statement



Two infinite-plane non-conducting, thin sheets of uniform surface charge p1 = 13.35 uC/m2 and p2 = -8.65 uC/m2) are parallel to each other and d = 0.245 m apart. (As shown in the diagram below.) What is the electric field between the sheets? (Note: the field is positive if it is parallel to the vector x).

prob18a.gif


Homework Equations



Sigma/2*epsilon_not

Epsilon not = 8.85e-12 (SI Units)

The Attempt at a Solution



The distance between the sheets should not matter in calculating the E-field between them because the E-field between them is uniform. We are given two sigmas and since the net charge on the field is toward the negative plane we just sum the two over 2*epsilon_not, and Epsilon not is a constant.

sigma1=13.35e-6 C/m^2
sigma2=-8.65e-6 C/m^2

(sigma1 + sigma2)/(2*epsilon_not) = E-field
(13.35e-6 + 8.65e-6)/(2*epsilon_not) = 1.2e6 N/C
Than since the E-field is perpendicular to the planes, but pointing in the opposite direction of positive X the answer becomes negative.
Answer: -1.2e6 N/C (unfortunately I tried this and did not get the problem right)

What did I get wrong?
 
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  • #2
In the region between the sheets:
What is the direction of the E field due to the σ1 sheet?

What is the direction of the E field due to the σ2 sheet?​
 
  • #3
The E-field on sigma1 is going -x and so is sigma2 right?
 
  • #4
Is the marking software fussy about significant figures?
 
  • #5
aximwolf said:
The E-field [STRIKE]on[/STRIKE] due to sigma1 is going -x and so is sigma2 right?

Right, so you should have a negative plus a negative.
 
  • #6
Right but that doesn't change the answer numerically am I forgetting a step?
 
  • #7
aximwolf said:
Right but that doesn't change the answer numerically am I forgetting a step?
Why did you express your answer to only 2 sig figs? (To repeat what gneill already pointed out.)
 
  • #8
More sig figs worked thank you everyone!
 
  • #9
aximwolf said:
Right but that doesn't change the answer numerically am I forgetting a step?
You have:
E-field due to sigma1=13.35e-6 C/m2
E-field due to sigma2=-8.65e-6 C/m2


But, if they're both pointing left (as vectors), then they should both be negative !

E1 + E2 = -13.35×10-6 + -8.65×10-6 = ____ ?
 
  • #10
yes that's the way I ended up doing it -13.35e-6+-8.65e-6
 
  • #11
That's stange, I don't see that result anywhere in this thread.
 

Related to Finding the E-field between two infinite plane charged sheets

1. What is the definition of an E-field between two infinite plane charged sheets?

The E-field, or electric field, is a vector field that describes the strength and direction of the electric force experienced by a charged particle at any point in space. In the case of two infinite plane charged sheets, the E-field is the force per unit charge experienced by a test charge placed between the two sheets.

2. How is the E-field between two infinite plane charged sheets calculated?

The E-field between two infinite plane charged sheets can be calculated using the formula E = σ/2ε0, where σ is the surface charge density of the sheets and ε0 is the permittivity of free space. This formula assumes that the sheets are parallel and infinitely large, and the distance between them is much smaller than the length of the sheets.

3. What factors affect the magnitude and direction of the E-field between two infinite plane charged sheets?

The magnitude and direction of the E-field between two infinite plane charged sheets are affected by the surface charge density of the sheets, the distance between them, and the permittivity of free space. Additionally, the orientation and location of the test charge placed between the sheets can also affect the E-field.

4. How does the E-field between two infinite plane charged sheets change as the distance between them increases?

As the distance between two infinite plane charged sheets increases, the magnitude of the E-field decreases. This is because the electric force experienced by a test charge decreases as the distance between the sheets increases, according to the inverse square law. However, the direction of the E-field remains the same, pointing from the positively charged sheet to the negatively charged sheet.

5. Can the E-field between two infinite plane charged sheets ever be zero?

Yes, the E-field between two infinite plane charged sheets can be zero if the two sheets have equal and opposite surface charge densities. This will result in the electric forces on a test charge being equal and opposite, canceling each other out and resulting in a net electric force of zero. However, this is a rare scenario as it requires precise balancing of the surface charge densities.

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