Calculating Speed of Block with Dielectric in Capacitor

In summary, the problem involves a horizontal square plate capacitor with a dielectric material, attached to a block via a massless string and pulley. The question asks for the speed of the block when the dielectric leaves the capacitor, given that the block starts at rest and the voltage across the capacitor is measured to be 500 V. Using the equations for energy and solving for the velocity, the answer is calculated to be 0.4 m/s. However, the actual answer is 4.4091 m/s, taking into account the change in potential energy of the block.
  • #1
123yt
32
0

Homework Statement


Consider a horizontal square plate capacitor of area 1*1 m2, capacitance in vacuum 2 uF, which contains a dielectric material with dielectric constant K=5. The dielectric slides frictionlessly and is attached via a massless string and a massless pulley to a block of mass 2.5 kg. The block pulls the dielectric from the capacitor as it falls. Compute the speed of the block at the instant the dielectric leaves the capacitor assuming it starts at rest and that the voltage across the capacitor after the dielectric is removed is measured to be 500 V.


Homework Equations


U = 1/2 CV^2 = q^2 / 2C


The Attempt at a Solution


Energy without dielectric = 1/2 * 2 * 10^-6 * 500^2 = 0.25
Energy with dielectric = 0.25 / k = 0.05

Energy change = 0.25 - 0.05 = 0.2

0.2 = 1/2 mv^2
v^2 = 0.4 / 2.5
v = 0.4 m/s

Actual answer is 4.4091 m/s .
 
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  • #2
123yt said:
Energy change = 0.25 - 0.05 = 0.2

Do not forget the change of the potential energy of the box.

ehild
 

1. What is a dielectric material?

A dielectric material is a type of insulating material that does not conduct electricity. It is commonly used in electronic devices to separate and protect electrical components.

2. How do dielectric materials store energy?

Dielectric materials store energy by creating an electric field when placed in an electric field. As the electric field increases, the molecules in the dielectric material become polarized, storing energy in the form of electric potential energy.

3. What is the difference between a dielectric and a conductor?

A dielectric material does not allow the flow of electric current, while a conductor does. This is due to the difference in the movement of electrons in each material. In a conductor, electrons are free to move, while in a dielectric, they are bound to their atoms.

4. How does the dielectric constant affect the energy storage capacity of a material?

The dielectric constant, also known as relative permittivity, is a measure of a material's ability to store electrical energy. A higher dielectric constant means a material can store more energy in an electric field compared to a material with a lower dielectric constant.

5. What are some common applications of dielectric materials?

Dielectric materials are used in a variety of applications, including capacitors, insulating coatings, and electrical cables. They are also used in medical devices, such as MRI machines, and in the production of solar cells and batteries.

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