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

Click For Summary
SUMMARY

The line integral of the magnetic field in a parallel-plate capacitor with a current of 20 A is calculated using the formula B = (μI)/(2πr). In this scenario, the integration path is a circle with a radius of 15 cm, located between the capacitor plates with an area of 0.80 m². The integration process involves substituting dl with 2πr and leads to complications when approaching ln(0), indicating a need for careful consideration of the integration limits. Understanding displacement current is crucial for resolving these issues.

PREREQUISITES
  • Understanding of Ampère's Law
  • Familiarity with magnetic field calculations
  • Knowledge of line integrals in vector calculus
  • Concept of displacement current in electromagnetism
NEXT STEPS
  • Study the derivation and application of Ampère's Law in different geometries
  • Learn about the concept of displacement current in detail
  • Explore advanced topics in electromagnetic theory, focusing on Maxwell's equations
  • Practice solving line integrals in various electromagnetic contexts
USEFUL FOR

Students and professionals in physics, particularly those studying electromagnetism, electrical engineers, and anyone involved in analyzing magnetic fields in capacitive systems.

Joe626
Messages
14
Reaction score
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 :)
 
Physics news on Phys.org
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:
thanks i understand it now :)
 

Similar threads

Two different dielectrics between parallel-plate capacitor
  • · Replies 6 ·
Replies
6
Views
2K
Charge on inner/outer surfaces of two large parallel conducting plates
  • · Replies 11 ·
Replies
11
Views
4K
Derivation Of Torque On Current Loop Due To Uniform Magnetic Field
  • · Replies 4 ·
Replies
4
Views
2K
Electric field between two parallel plates
  • · Replies 58 ·
2
Replies
58
Views
6K
Magnetic Field in parallel plate capacitor
  • · Replies 12 ·
Replies
12
Views
7K
Final potential difference of a 2 capacitor system
  • · Replies 3 ·
Replies
3
Views
3K
Electric and Magnetic field acting on an electron
  • · Replies 25 ·
Replies
25
Views
6K
Line Integral to Verify the Magnetic Field B
  • · Replies 10 ·
Replies
10
Views
2K
Find the charge on the plates of a parallel-plate capacitor w/ dielectric
  • · Replies 3 ·
Replies
3
Views
2K
Magnitude of the induced magnetic field in a circuit
  • · Replies 5 ·
Replies
5
Views
4K