Cross Product of Antiparallel Vectors: qvXb Maybe Not?

In summary, we consider the example of a positive charge moving in the -z direction with speed v, with the local magnetic field of magnitude B in the +z direction. We use the equation F=qvXb to find the magnitude of the magnetic force acting on the particle, and express the answer in terms of q, v, B, and other given quantities. However, this equation only works when v and B are orthogonal, not antiparallel. A reminder to refer back to the definition of the cross product is given, and the speaker acknowledges that these concepts can be confusing at times.
  • #1
SoulofLoneWlf
29
0
qvxb maybe not??

Homework Statement


consider the example of a positive charge moving in the -z direction with speed with the local magnetic field of magnitude in the +z direction. Find , the magnitude of the magnetic force acting on the particle.
Express your answer in terms of , , , and other quantities given in the problem statement.


Homework Equations




f=qvXb yet this does not work ;/
This would be true if and were orthogonal. Instead, they are antiparallel--look back at the definition of the cross product if you still have trouble.

The Attempt at a Solution

 
Physics news on Phys.org
  • #2


SoulofLoneWlf said:
f=qvXb yet this does not work ;/
This would be true if and were orthogonal.
[tex]\vec{F} = q\vec{v}\times \vec{B}[/tex]

works just fine, but that only equals qvB when v and B are orthogonal.
Instead, they are antiparallel--look back at the definition of the cross product if you still have trouble.
Sounds like good advice to me.
 
  • #3


Doc Al said:
[tex]\vec{F} = q\vec{v}\times \vec{B}[/tex]

works just fine, but that only equals qvB when v and B are orthogonal.

Sounds like good advice to me.

thank these things just confuse me at time :) lol easy to study for hard to do some how :/
 

1. What is the definition of a cross product?

A cross product is a mathematical operation that takes two vectors as input and produces a new vector that is perpendicular to both of the input vectors.

2. How is the cross product of two vectors calculated?

The cross product of two vectors, q and b, is calculated using the following formula: qvXb = |q||b|sin(theta)n, where |q| and |b| are the magnitudes of the vectors, theta is the angle between them, and n is a unit vector perpendicular to both q and b.

3. What does it mean for two vectors to be antiparallel?

Two vectors are antiparallel if they are parallel but in opposite directions. This means that the angle between them is 180 degrees and the cross product will be zero.

4. Can the cross product of two antiparallel vectors ever be non-zero?

No, the cross product of two antiparallel vectors will always be zero because the angle between them is 180 degrees, resulting in a zero value for the sine function in the cross product formula.

5. Why is the cross product of antiparallel vectors sometimes referred to as "qvXb Maybe Not"?

The term "qvXb Maybe Not" is used to emphasize the fact that the cross product of antiparallel vectors may not always be a valid operation. While the mathematical definition of the cross product includes the calculation of a perpendicular vector, this is not possible when the input vectors are antiparallel. Therefore, the result is technically undefined or "maybe not" a valid vector.

Similar threads

Replies
10
Views
646
  • Linear and Abstract Algebra
Replies
32
Views
3K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
874
  • Introductory Physics Homework Help
Replies
4
Views
5K
Replies
8
Views
778
  • Introductory Physics Homework Help
Replies
9
Views
1K
Replies
14
Views
1K
  • Introductory Physics Homework Help
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
3K
Back
Top