Magnetic field vector using F = qV * B

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Homework Help Overview

The discussion revolves around finding the magnetic field vector B using the equation F = qV × B, where participants are working with a three-dimensional vector context. The original poster presents specific values for force, velocity, and charge, expressing confusion about resolving the vector equation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants suggest breaking down the force vector into its components and writing individual equations for each component. There is also a discussion about the correctness of the charge value and its implications. Some participants attempt to express the relationship between the vectors in matrix form, while others question the clarity of these representations.

Discussion Status

The discussion is ongoing, with participants providing guidance on how to approach the problem by focusing on the components of the vectors involved. There is recognition of the complexity in the original poster's representation, and suggestions to clarify the equations being used. Multiple interpretations of the vector relationships are being explored, but no consensus has been reached.

Contextual Notes

Participants note the assumption that Bx = 0, which influences the discussion about the components of the magnetic field vector. There is also mention of the need for additional information to solve for B definitively, as the cross product only provides certain components of B.

happyparticle
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Homework Statement
Magnetic field
Relevant Equations
F = qV * B.
Hi,
I'm trying to find the magnetic field B using F = qV * B.
I have F = (3i + j + 2k) N
V = (-i +3j) * 10^6 m/s
q = -2 *10^6 C
Bx = 0

I don't know how to resolve a 3 dimensional vector equation.
B = F/qV makes not sense for me.
 
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Work with the components of F. That is, write out individual equations for Fx, Fy, and Fz.

Is the factor of 106 correct for q? That's a LOT of charge :wideeyed:
 
TSny said:
Work with the components of F. That is, write out individual equations for Fx, Fy, and Fz.

Is the factor of 106 correct for q? That's a LOT of charge :wideeyed:
10^-6, my bad.
 
qV = (2i -6j)

(2i -6j) * B = (3i + j + 2k)I tried something, but I don't if it is the right way.

2 0 = 3
-6 j = 1
0 k = 2
then,
-6k = 3
-2k = 1
2j = 2

k =-0.5 and j = 1
B = `(j - 0.5k) T
 
I agree with your final result, but I can't follow your work.

For example, you wrote:
EpselonZero said:
2 0 = 3
-6 j = 1
0 k = 2

On the left of the first equation, you wrote 2 0. What does this mean?

On the left of the second equation, you wrote - 6 j. Is this -6 multiplied by the unit vector j? How can that equal the right hand side, which is equal to 1?
 
It's quite impossible to type it. Basically, it's like a matrix 2i 0i | 3
-6i j | 1
0i k| 2
 
EpselonZero said:
It's quite impossible to type it. Basically, it's like a matrix 2i 0i | 3
-6i j | 1
0i k| 2
I still can't follow this. You got the correct answer, so I think you are probably thinking about it correctly. I just can't follow the way you are writing it.

I was suggesting that you write an equation for just the x-component of the vector equation ##\vec F = q \vec v \times \vec B##.

Thus,

Fx = ...

where the right-hand side would be expressed in terms of q and certain components of v and B.
 
I'm not sure to understand. Fx = 3i
3i = 2i ?
 
EpselonZero said:
I'm not sure to understand. Fx = 3i
3i = 2i ?
When you take the cross product of two vectors, ##\vec b \times \vec c##, the x-component of the cross product is

##(\vec b \times \vec c )_x = b_yc_z -b_zc_y##.

Similarly for the y and z components. See here. This pattern is worth memorizing!

Use this to write out the x-component of the vector equation ##\vec F = q \vec V \times \vec B##. That is, write out the right-hand side of

##F_x = q (\vec V \times \vec B)_x##
 
  • #10
You cannot solve for ##\vec B## from the magnetic force equation unless you know the force for more than one velocity. The cross product contains information only about the components of ##\vec B## that are perpendicular to ##\vec v##. However, you have additional information as you know that ##B_x = 0##.

a) What does this tell you about ##\vec B##?
b) what do you then get if you take the inner product of ##\vec F## and ##\vec B##?
 

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