Capacitor Problem involving a slab of Copper between a Capacitor

In summary, the problem involves a slab of copper being inserted into a parallel-plate capacitor with a charge of 1.00×10-6 C and a gap of 10.0 mm. The ratio of stored energy before to after insertion can be found by calculating the capacitance equivalent of c1 and c2, which are equal due to the same area and distance. This results in c1 being divided by 2, and the value of c1 can be found using the formula (epsilon nought * Area)/ distance. It is important to halve the distance, d-b, in order to get the correct answer.
  • #1
Simon777
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Homework Statement


A slab of copper of thickness b = 1.370 mm is thrust into a parallel-plate capacitor of C = 9.00×10-11 F of gap d = 10.0 mm, as shown in the figure; it is centered exactly halfway between the plates.

If a charge q = 1.00×10-6 C is maintained on the plates, what is the ratio of the stored energy before to that after the slab is inserted?


I already know how to solve this problem. I just have a question about one of the steps. You need to find capacitance equivalent of c1 and c2 and since area and distance are the same, c1=c2. You end up with

C equivalent= c1/2

Now c1= (epsilon nought * Area)/ distance

so you just plug this in

Why do I only get the right answer when the distance is d-b? If you are just referring to c1, shouldn't it be half of d-b? Why use the combined distance of capacitor 1 and 2?
 
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  • #2
Nevermind, I figured it out. I had to half d-b just like I thought. For some reason I unknowingly halved d-b and got the right answer and confused myself.
 

1. What is a capacitor and how does it work?

A capacitor is an electronic component used to store and release electrical energy. It consists of two conductive plates separated by an insulating material, known as a dielectric. When a voltage is applied to the capacitor, it charges the plates, creating an electric field between them. This electric field stores the energy and can be discharged when needed.

2. How does a slab of copper affect the capacitance of a capacitor?

A slab of copper placed between the plates of a capacitor acts as a dielectric material. This dielectric increases the capacitance of the capacitor by reducing the electric field between the plates. The higher the dielectric constant of the material, the greater the increase in capacitance.

3. What factors affect the capacitance of a capacitor with a slab of copper?

The capacitance of a capacitor with a slab of copper is affected by the thickness of the copper slab, the area of the plates, and the distance between the plates. The dielectric constant of the copper slab also plays a significant role in determining the capacitance.

4. How can I calculate the capacitance of a capacitor with a slab of copper?

The capacitance of a capacitor with a slab of copper can be calculated using the formula C = εA/d, where C is the capacitance, ε is the dielectric constant of the copper slab, A is the area of the plates, and d is the distance between the plates. This formula assumes a parallel plate capacitor with a uniform electric field.

5. What are some real-world applications of a capacitor with a slab of copper?

A capacitor with a slab of copper is commonly used in electronic devices such as power supplies, audio equipment, and electric motors. It is also used in energy storage systems, such as in hybrid and electric vehicles. Additionally, capacitors with copper slabs are used in electronic circuits to filter or block certain frequencies of signals.

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