Ampere-Maxwell Law: Voltage Application Explained

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In summary, the conversation discusses an example in a book involving two metal cylinders with a distance between them. The problem involves an applied voltage between the plates, which is represented by a sin(kt) term in the V(t) equation. The conversation also clarifies the difference between an oscillating voltage and a capacitor being charged at a constant rate by a steady current, and introduces the concepts of capacitance and current.
  • #1
ronaldoshaky
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Hello to all. I am looking at an example in my book (again. =O)

The example has two metal cylinders with a distance, d between them

The problem states that a voltage V(t) is applied between the plates.

What do they mean by that?

(I thought it was an oscillating voltage, since they have a sin(kt) term in the V(t) equation. Is that different from the capacitor being charged at a constant rate by a steady current).
 
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  • #2
Recall that the charge Q in a cylindrical capacitor is

Q(t) = C·V(t)

where C is the capacitance and V(t) is the applied voltage. differentiating, we get the current I(t):

I(t) = C·dV(t)/dt

Bob S
 
  • #3
I see. Thanks
 

1. What is the Ampere-Maxwell Law?

The Ampere-Maxwell Law is a fundamental law in electromagnetism that describes the relationship between the magnetic field and the electric current in a closed 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 the permittivity of free space.

2. How is the Ampere-Maxwell Law applied in voltage calculations?

The Ampere-Maxwell Law is used to calculate the voltage induced in a circuit due to a changing magnetic field. By taking the line integral of the magnetic field around a closed loop, the induced voltage can be determined using the equation V = -dΦ/dt, where V is the induced voltage, Φ is the magnetic flux, and t is time.

3. What is the relationship between the Ampere-Maxwell Law and Faraday's Law?

Faraday's Law states that a changing magnetic field can induce an electric field, while the Ampere-Maxwell Law relates the magnetic field to the electric current. These two laws are closely related and are often used together in electromagnetism calculations.

4. What is the significance of the permittivity of free space in the Ampere-Maxwell Law?

The permittivity of free space, denoted by the symbol ε0, is a fundamental constant that relates the electric field to the electric charge in a vacuum. In the Ampere-Maxwell Law, it is used to convert the magnetic field line integral to the induced voltage, allowing for the calculation of the electric field in a circuit.

5. How does the Ampere-Maxwell Law explain the behavior of electromagnetic waves?

The Ampere-Maxwell Law is one of the four Maxwell's equations, which together describe the behavior of electromagnetic waves. This law explains how changing electric fields can induce magnetic fields and vice versa, allowing for the propagation of electromagnetic waves through space.

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