Solve Ampere's Law & Displacement Current: Capacitor Voltage Change

  • Thread starter airkapp
  • Start date
  • Tags
    Maxwell
In summary, Ampere's Law is a fundamental law in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through the loop. To solve for the magnetic field, one must determine the direction of the magnetic field around the loop, calculate the line integral, and use the equation B = (μ0 * I) / (2 * π * r). Displacement current is a concept that explains how changing electric fields can induce magnetic fields and is crucial in understanding capacitors and electromagnetic waves. It is directly related to the rate of change of voltage in a capacitor. To solve for the voltage change in a capacitor, one must calculate the displacement current, use Ampere's Law to determine the magnetic field, and
  • #1
airkapp
58
0
Ampere's Law and Displacement Current...anybody?

Determine the rate at which the electric field changes between the round plates of a capacitor, 6.0 cm in diameter, if the plates are spaced 1.3 mm apart and the voltage across them is changing at a rate of 120V/s

I found area:

A = 2πr2 = 2 π(.03 m)2

= .006 m

then do I solve for dE/dt ?
 
Last edited:
Physics news on Phys.org
  • #2
Why do you need area to find E?
 
  • #3


Yes, you can solve for the rate of change of electric field (dE/dt) using the equation for displacement current, which is given by:

dE/dt = (I_d)/(Aε_0)

Where I_d is the displacement current, A is the area between the plates, and ε_0 is the permittivity of free space.

In this case, the displacement current can be calculated using Ampere's Law, which states that the line integral of the magnetic field around a closed loop is equal to the current passing through the loop. Since there is no current passing through the loop, the displacement current is equal to the rate of change of electric field.

Therefore, we can rewrite the equation as:

dE/dt = (μ_0I)/A

Where μ_0 is the permeability of free space.

Now, we can plug in the given values:

dE/dt = (μ_0(120V/s))/(.006 m)

= 2.0 x 10^-4 T/s

This is the rate at which the electric field is changing between the plates of the capacitor.
 

1. What is Ampere's Law?

Ampere's Law is a fundamental law in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through the loop. It states that the line integral of the magnetic field around a closed loop is equal to the current passing through the loop, multiplied by a constant called permeability of free space.

2. How do you use Ampere's Law to solve for the magnetic field?

To use Ampere's Law to solve for the magnetic field, you must first determine the direction of the magnetic field around the closed loop. Then, you need to determine the current passing through the loop and calculate the line integral of the magnetic field. Finally, you can use the equation B = (μ0 * I) / (2 * π * r) to solve for the magnitude of the magnetic field at a specific distance from the current-carrying wire.

3. What is displacement current?

Displacement current is a concept introduced by James Clerk Maxwell to explain how changing electric fields can induce magnetic fields. It is not an actual current of moving charges, but rather the rate of change of electric flux through a surface. It plays a crucial role in the laws of electromagnetism and is a key factor in understanding the behavior of capacitors and electromagnetic waves.

4. How is displacement current related to capacitor voltage change?

In a capacitor, displacement current flows between the plates as the electric field between them changes. This displacement current is directly related to the rate of change of the voltage across the capacitor. As the voltage across the capacitor increases or decreases, the displacement current also changes, leading to a change in the electric and magnetic fields between the plates.

5. How can I solve for the voltage change in a capacitor using Ampere's Law and displacement current?

To solve for the voltage change in a capacitor using Ampere's Law and displacement current, you must first calculate the displacement current flowing between the plates. Then, you can use Ampere's Law to determine the magnetic field created by this displacement current. Finally, you can use the relationship between the electric and magnetic fields to solve for the change in voltage across the capacitor. This process is also known as "charging" or "discharging" a capacitor.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
664
Replies
2
Views
660
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
29
Views
2K
Replies
1
Views
4K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
8K
  • Introductory Physics Homework Help
Replies
2
Views
2K
Back
Top