Electric field of a disk & u-substitution

Click For Summary
SUMMARY

The discussion focuses on calculating the electric field at point P due to a disk using u-substitution in integration. The participant clarifies that the limits of integration for the u-integral are derived from the relationship between the variable r and u, specifically stating that the lower limit corresponds to u = x² when r = 0, and the upper limit is u = x² + R². This understanding is crucial for correctly setting up the integral to solve the problem effectively.

PREREQUISITES
  • Understanding of electric fields and their calculations
  • Familiarity with integration techniques, specifically u-substitution
  • Knowledge of calculus, particularly limits of integration
  • Basic physics concepts related to electrostatics
NEXT STEPS
  • Study the application of u-substitution in multiple integrals
  • Explore electric field calculations for different geometries, such as disks and spheres
  • Review the principles of electrostatics and Gauss's Law
  • Practice solving problems involving limits of integration in calculus
USEFUL FOR

Students studying physics and mathematics, particularly those focusing on electromagnetism and calculus, as well as educators looking for problem-solving techniques in electric field calculations.

Taulant Sholla
Messages
96
Reaction score
5

Homework Statement


Calculate the electric field at point P (refer to visual):
Capture.JPG


Homework Equations


I follow everything - except how the limits of integration for the u-integral (
Capture1.JPG
) are arrived at?

The Attempt at a Solution


u=x2 is the smallest value u can have, and u=x2+R2 is the greatest value u can have?
 
Physics news on Phys.org
The lower limit of the u integration should correspond to the lower limit of the r integration (r = 0). So, the lower limit of the u integration is the value of u when r = 0. Similarly for the upper limit.
 
Very helpful - thank you!
 

Similar threads

Replies
4
Views
3K
Replies
9
Views
2K
Replies
9
Views
905
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
1
Views
2K
  • · Replies 23 ·
Replies
23
Views
2K
Replies
1
Views
1K
Replies
9
Views
3K
  • · Replies 3 ·
Replies
3
Views
7K