Simple calculation about Magnetic induction

Click For Summary
SUMMARY

The discussion centers on the calculation of magnetic induction, specifically addressing why a certain term in the equation becomes zero. The term in question is related to the gradient of the function defined by the vector ##\vec{V} = \vec{\nabla} \left ( \frac{1}{|\vec{x}-\vec{x}'|} \right )##. It is established that the derivative ##\nabla## operates with respect to the variable ##\vec{x}##, not ##\vec{x}'##, leading to the conclusion that the second term does not exist in this context.

PREREQUISITES
  • Understanding of vector calculus, particularly gradient operations.
  • Familiarity with magnetic induction concepts in physics.
  • Knowledge of mathematical notation and vector identities.
  • Basic proficiency in solving differential equations.
NEXT STEPS
  • Study vector calculus, focusing on gradient and divergence operations.
  • Explore magnetic induction principles in electromagnetism.
  • Review vector identities and their applications in physics.
  • Practice solving differential equations related to physical systems.
USEFUL FOR

Students of physics, particularly those studying electromagnetism, as well as educators and anyone involved in advanced mathematics or engineering disciplines.

BREAD
Messages
50
Reaction score
0

Homework Statement


upload_2017-5-10_18-45-30.png


Homework Equations

The Attempt at a Solution


upload_2017-5-10_18-45-50.png


Why does the second term become zero??
 
Physics news on Phys.org
BREAD said:
Why does the second term become zero??
Because it does not exist. If, in the previous equation, you substitute the gradient with some vector ##\vec{V} = \vec{\nabla} \left ( \frac{1}{|\vec{x}-\vec{x}'|} \right )##, you will see why. There is no vector identity in the front of the book to be used.
 
BREAD said:
Why does the second term become zero?
The derivative ##\nabla## is with respect to ##\vec{x}##, not ##\vec{x}'##.
 
Last edited:

Similar threads

EM: Separation of variables to find magnetic induction
  • · Replies 8 ·
Replies
8
Views
2K
Calculate superconductor's magnetic susceptibility from Inductance
  • · Replies 1 ·
Replies
1
Views
2K
How to Calculate the Cyclotron Magnetic Dipole Moment in a Penning Trap?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad How induction works within a coil (nuances of it)
  • · Replies 6 ·
Replies
6
Views
2K
Calculate inductance of finite Solenoid
  • · Replies 1 ·
Replies
1
Views
5K
Engineering Inductance of a layered Solenoid?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Need a good idea : 3D simulation of Inductive wireless power transfer
  • · Replies 6 ·
Replies
6
Views
2K
Moving magnetic dipole into current loop
  • · Replies 1 ·
Replies
1
Views
2K
Explaining the Inconsistency and Solution in Faraday's Law of Induction
  • · Replies 6 ·
Replies
6
Views
3K
High School What is the difference between B and H?
  • · Replies 14 ·
Replies
14
Views
4K