Cartesian Coordinates and Cross Product of Vectors for Magnetic Field Direction?

Click For Summary

Homework Help Overview

The discussion revolves around understanding the cross product of vectors in Cartesian coordinates, particularly in the context of determining the direction of the magnetic field. Participants are exploring the implications of the right-hand rule and the orientation of unit vectors.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the sign of the cross product result and its relation to the right-hand rule. There is also a discussion about the ambiguity in the problem regarding the position of a charge relative to two wires and how that might affect the magnetic field direction.

Discussion Status

Some participants have provided insights into the right-hand rule and the orientation of unit vectors, while others are raising questions about the clarity of the problem statement and its implications on the magnetic field direction. Multiple interpretations of the problem are being explored.

Contextual Notes

The original problem lacks specificity regarding the position of the charge in relation to the wires, which may lead to different interpretations of the magnetic field direction. Participants are also considering the potential confusion arising from the problem's wording.

The black vegetable
Messages
22
Reaction score
0

Homework Statement


upload_2017-2-10_15-9-0.png


Homework Equations

The Attempt at a Solution


upload_2017-2-10_15-10-26.png


the answer given is the same but without the negative sign, I don't understand because the crossproduct of unit vectors
upload_2017-2-10_15-13-41.png

when using a Cartesian coordinates of the directions given by the right-hand rule? Is the positive z direction pointing out of the page if X and Y are as follows
upload_2017-2-10_15-18-3.png

apologies if this is in the wrong section, thanks for any help in advance
 
Physics news on Phys.org
Yes. ##\hat {k} = \hat {\bf \imath } \times\hat {\bf \jmath}## , so z points towards you, out of the screen.

Corkscrew rule I call it. Turn ##\hat{\bf \imath }## over the smallest angle towards ##\hat {k}##. Corkscrew will go in the minus y direction : $$\hat \imath \times\hat k = -\hat \jmath $$
 
The problem doesn't specify which of the two wires the charge -q is a distance b from. Does the answer change if you pick the other wire to be a distance b from -q?
 
  • Like
Likes   Reactions: BvU
Thank you both your answers, TSny I thought the same, closer to the top wire the combined magnetic field would be in the opposite direction . Maybe the question is just not very good
 

Similar threads

Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 6 ·
Replies
6
Views
5K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 12 ·
Replies
12
Views
2K
Replies
13
Views
2K
  • · Replies 25 ·
Replies
25
Views
4K
  • · Replies 2 ·
Replies
2
Views
4K