The Magnetic Field in a Charging Capacitor problem

In summary, the conversation discusses the calculation of the magnetic field inside a parallel-plate capacitor with circular plates charged by a constant current. Using Ampère's law as extended by Maxwell, one can pick an amperian surface and calculate either current or electric flux through that surface to determine the value of the right side of the equation. This can then be used to solve for B, the magnitude of the magnetic field inside the capacitor as a function of distance from the axis joining the center points of the circular plates. The solution should be expressed in terms of mu_0 and given quantities.
  • #1
cupcake
76
0
A parallel-plate capacitor of capacitance C with circular plates is charged by a constant current I. The radius a of the plates is much larger than the distance d between them, so fringing effects are negligible. Calculate B(r), the magnitude of the magnetic field inside the capacitor as a function of distance from the axis joining the center points of the circular plates.

Express your answer in terms of mu_0 and given quantities.

according to Ampère's law as extended by Maxwell:
[tex]

\oint \vec{B} \cdot d\vec{l}= \mu_0\left(I+ \epsilon_0 \frac{d\Phi}{dt}\right).

[/tex]


what should i do then?
please advise...
 
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  • #2
anyone can help me?
 
  • #3
Pick an amperian surface, and calculate either current or electric flux through that surface. That will give you the value of the right side of the equation. Then solve for B.
 
  • #4
nealh149 said:
Pick an amperian surface, and calculate either current or electric flux through that surface. That will give you the value of the right side of the equation. Then solve for B.

how to calculate flux through the that surface??
 

Related to The Magnetic Field in a Charging Capacitor problem

1. What is a charging capacitor?

A charging capacitor is a device that stores electrical energy in the form of an electric charge. It is composed of two conductive plates separated by an insulating material, known as a dielectric. When a voltage is applied to the capacitor, one plate collects a positive charge and the other collects a negative charge, creating an electric field between them.

2. How does a charging capacitor produce a magnetic field?

When a capacitor is charging, an electric current flows from one plate to the other. This flow of current creates a changing magnetic field around the capacitor. According to Maxwell's equations, a changing electric field produces a magnetic field, and vice versa. Therefore, the changing electric field in a charging capacitor produces a magnetic field.

3. What factors affect the strength of the magnetic field in a charging capacitor?

The strength of the magnetic field in a charging capacitor is affected by several factors, including the voltage applied to the capacitor, the distance between the plates, the surface area of the plates, and the material of the dielectric. Generally, the higher the voltage and the closer the plates are together, the stronger the magnetic field will be.

4. Is the magnetic field in a charging capacitor constant?

No, the magnetic field in a charging capacitor is not constant. As the capacitor charges, the electric field between the plates increases, causing the magnetic field to also increase. Once the capacitor is fully charged, the electric field and magnetic field are at their maximum. When the capacitor is discharging, the magnetic field decreases until it reaches zero when the capacitor is fully discharged.

5. How is the magnetic field in a charging capacitor used in practical applications?

The magnetic field in a charging capacitor can be used in a variety of practical applications, including energy storage, filtering and smoothing of electrical signals, and in electronic circuits. Capacitors are also used in many electronic devices such as computers, cameras, and cell phones to store and regulate electrical energy.

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