Dielectric Problem: Q&A to Calculate Electric Field & Induced Charge

[at3rg0]

Homework Statement

Two parallel plates have charges Q and -Q. When the space between the plates is devoid of matter, the electric field is 2.7E5 V/m. When the space is filled with a certain dielectric, the field is reduced to 1.3E5 V/m.

What is the dielectric constant of the dielectric?
I got this answer as 2.07692, which was correct.

If Q = 8 nC, what is the area of the plates?
I tried plugging the numbers into the formulas below, but I'm not getting the right answer...Am I missing a piece of relevant information?

What is the total induced charge on either face of the dielectric?
This will be easier once I figure out the second question.

Homework Equations

E=E(not)/kappa
V=Ed
C=Q/V
C=epsilon(not)*kappa*Area/distance

The Attempt at a Solution

I got the first answer, and the second I could not get.

 

[dynamicsolo]

The Attempt at a Solution

I got the first answer, and the second I could not get.

It is more helpful to someone wishing to assist you if you show your calculation so they can see what you set up and what values you got. Thanks.

P.S. Are you given a plate separation distance?

 

[at3rg0]

Using the formulas, I got that

Area = Q*Epsilon(not)/Electric Field

So Area = (8E-9)(8.85E-12)/1.3E5 = 5.45E-25 m^2 (so 5.45E-23cm^2) - I need to give the answer in cm^2.

 

[dynamicsolo]

Using the formulas, I got that

Area = Q*Epsilon(not)/Electric Field

So Area = (8E-9)(8.85E-12)/1.3E5 = 5.45E-25 m^2 (so 5.45E-23cm^2) - I need to give the answer in cm^2.

The units on the right hand side are presently (C)·(C^2/N·m^2)/(N/C), so I don't think this is going to give you an area.

OK, you don't need a plate separation, but I suggest you review how you rearranged your equations to get Area...

 

[at3rg0]

Going by units alone...

Shouldn't Q/(Epsilon0 * E) give m^2?

All right, I tried rearranging again.

A = C/(Epsilon0*E*kappa), which gives me .003762. Where am I making the mistake in formula manipulation?

I used C=Q/V, where V=Ed, and C=kappa*epsilon0*Area/d

 

[dynamicsolo]

Going by units alone...

Shouldn't Q/(Epsilon0 * E) give m^2?

All right, I tried rearranging again.

A = C/(Epsilon0*E*kappa), which gives me .003762. Where am I making the mistake in formula manipulation?

I used C=Q/V, where V=Ed, and C=kappa*epsilon0*Area/d

This is fine now. You set

C = (kappa·eps0·A)/d = Q/V , so

A = (Q · d)/(kappa · eps0 · V) , but E = V / d , so

A = Q / (kappa · eps0 · E).

The units are C / [ {(C^2)/N·(m^2)} · {N/C} ] = C / [C/(m^2)] = m^2 .

I also get your value, but it looks small because it's in m^2, so A = 33.6 cm^2. (What are you using for epsilon_0 ?)