Calculating Force per Unit Area on Dielectric due to Capacitor

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In summary, the question is asking for the force per unit area exerted by the electric field on a dielectric in a plane capacitor. The formula for this is F/A = ε0E^2/2, where F is the force, A is the area, ε0 is the permittivity of free space, and E is the electric field strength. The electric field strength can be found using the formula E = σ/ε0k, where σ is the surface charge density and k is the dielectric constant. By substituting this into the first formula, we get F/A = (L0/ε0k)^2/2 = L0^2/2ε0^2k^2.
  • #1
atavistic
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Homework Statement



The space between the plates of a plane capacitor is filled with a dielectric of constant k. The plate gets a charge of surface density L_0 .

Determine the force per unit area that is exerted by the field on the dielectric.





2. The attempt at a solution

I found the bound charge density which came out to be L = L_0(1 -1/k)

Now I know the E inside the plates(without dielectric) is L_0/epsilon_0 and the field due to the induced charge of one side is L/2 epsilon_0 in the opposite direction . So I found net E(by superposition principle) , and multiplied by L i.e. charge per unit area.

But this doesn't match the answer.
 
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  • #2


Hello,

Thank you for your post. The force per unit area exerted by the electric field on the dielectric can be calculated using the following formula:

F/A = ε0E^2/2

Where F is the force, A is the area, ε0 is the permittivity of free space, and E is the electric field strength. In this case, the electric field strength can be found by using the following formula:

E = σ/ε0k

Where σ is the surface charge density and k is the dielectric constant. By substituting this into the first formula, we get:

F/A = (σ/ε0k)^2/2

= (L0/ε0k)^2/2

= L0^2/2ε0^2k^2

Therefore, the force per unit area exerted by the electric field on the dielectric is L0^2/2ε0^2k^2.

I hope this helps. Let me know if you have any further questions.
 
  • #3


I appreciate your attempt at solving this problem and using the appropriate equations. However, it seems like there may have been a mistake in your calculation or application of the equations. I recommend double checking your steps and equations to ensure accuracy. Additionally, it may be helpful to consult a textbook or other resources for a step-by-step guide on how to solve problems like this. Keep in mind that force per unit area is also known as pressure, so you may need to use equations related to pressure as well. Good luck with your homework!
 

1. What is force per unit area on a dielectric due to a capacitor?

Force per unit area on a dielectric due to a capacitor is the amount of force exerted on the dielectric material by the electric field created by the capacitor. It is also known as the electric stress or electric pressure.

2. How is the force per unit area on a dielectric calculated?

The force per unit area on a dielectric can be calculated by dividing the electric field strength by the permittivity of the dielectric material. The formula is F/A = E/ε, where F is the force, A is the area, E is the electric field strength, and ε is the permittivity of the dielectric material.

3. What is the unit of measurement for force per unit area on a dielectric?

The unit of measurement for force per unit area on a dielectric is Newtons per square meter (N/m²) in the SI system. In some other systems, it may be measured in pounds per square inch (psi) or dynes per square centimeter (dyn/cm²).

4. How does the dielectric material affect the force per unit area on a capacitor?

The permittivity of the dielectric material affects the force per unit area on a capacitor. The higher the permittivity, the stronger the electric field and therefore, the higher the force per unit area. Different dielectric materials have different permittivity values, which can affect the overall force on the dielectric in a capacitor.

5. Can the force per unit area on a dielectric be negative?

No, the force per unit area on a dielectric cannot be negative. It is always a positive value as it represents the force exerted on the dielectric by the electric field created by the capacitor. A negative value would indicate that the electric field is acting in the opposite direction, which is not possible.

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