What is the Line Integral of Magnetic Field in a Parallel-Plate Capacitor?

In summary, the given conversation discusses finding the value of the line integral B ∙ dl in a circuit with a current of 20 A and a parallel-plate capacitor with an area of 0.80 m2 and no dielectric. The integration path C is a 15-cm-radius circle lying parallel to the plates and within the region between them. The equation used is b = muI/2rPI, and the attempt at a solution involved changing dl to 2PIdr and integrating, resulting in an answer with ln(0). The solution is found by considering displacement current and can be further explored using the provided resources.
  • #1
Joe626
14
0

Homework Statement


There is a current of 20 A in a resistor that is connected in series with a parallel-plate capacitor. The plates of the capacitor have an area of 0.80 m2, and no dielectric exists between the plates. Find the value of the line integral B ∙ dl , where the integration path C is a 15-cm-radius circle that lies in a plane that is parallel with the plates and is completely within the region
between them.


Homework Equations


b = muI/2rPI,


The Attempt at a Solution



i changed dl to 2PIdr and integrated. ended up with something that included ln(0). it just seemed wrong. any help is appreciated :)
 
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  • #2
See,

http://www.physics.upenn.edu/courses/gladney/phys151/lectures/lecture_temp.html

http://www.cramster.com/answers-mar-08/physics/ampre-maxwell-law-find-line-integral-loop-radiu_217689.aspx

Have you learned about displacement current yet?
 
Last edited by a moderator:
  • #3
thanks i understand it now :)
 

1. What is an integrated magnetic field?

An integrated magnetic field is the total magnetic field present in a given region. It is a combination of the magnetic fields produced by all the sources in that region, including permanent magnets, electric currents, and charged particles.

2. How do you measure an integrated magnetic field?

An integrated magnetic field can be measured using a device called a magnetometer. This instrument detects and measures the strength and direction of the magnetic field at a specific location. The measurement is usually represented by a vector quantity, with the direction of the vector indicating the direction of the magnetic field and the magnitude representing the strength.

3. What are some common applications of integrating magnetic fields?

Integrating magnetic fields has numerous applications in various fields, including navigation, geophysics, and medical imaging. In navigation, the Earth's integrated magnetic field is used to determine the direction of a compass. In geophysics, integrated magnetic fields are used to study the composition and structure of the Earth's interior. In medical imaging, magnetic resonance imaging (MRI) uses integrated magnetic fields to produce images of the body's internal structures.

4. How do you integrate magnetic fields mathematically?

The mathematical integration of magnetic fields involves using the principles of vector calculus. The magnetic field is represented by a vector field, and the integration is performed by calculating a line integral over a closed path surrounding the sources of the magnetic field. This integration can be performed numerically using computer software or analytically using mathematical equations.

5. What factors can affect the integration of magnetic fields?

The integration of magnetic fields can be affected by various factors, including the distance from the source of the magnetic field, the strength and orientation of the magnetic field, and the presence of other magnetic fields. Additionally, the magnetic properties of the surrounding materials can also influence the integration of magnetic fields, as some materials can amplify or distort magnetic fields.

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