Magnetic field vector using F = qV * B

In summary, the magnetic force equation states that the force between two magnets is proportional to the product of their magnetic fields. However, you need additional information in order to solve for the magnetic field of a magnet. When you take the cross product of two vectors, the x-component of the cross product is equal to the y-component of the cross product minus the z-component of the cross product.
  • #1
happyparticle
410
20
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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  • #2
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:
 
  • #3
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.
 
  • #4
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
 
  • #5
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?
 
  • #6
It's quite impossible to type it. Basically, it's like a matrix 2i 0i | 3
-6i j | 1
0i k| 2
 
  • #7
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.
 
  • #8
I'm not sure to understand. Fx = 3i
3i = 2i ?
 
  • #9
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##?
 

Related to Magnetic field vector using F = qV * B

1. What is the formula for calculating the magnetic field vector using F = qV * B?

The formula for calculating the magnetic field vector using F = qV * B is the product of the charge of the particle (q), its velocity (V), and the strength of the magnetic field (B).

2. How does the direction of the magnetic field vector relate to the direction of the force on a charged particle?

The direction of the magnetic field vector is perpendicular to both the direction of the particle's velocity and the direction of the force acting on the particle. This means that the magnetic field vector is always at a 90 degree angle to the plane formed by the velocity and force vectors.

3. What is the unit of measurement for the magnetic field vector?

The unit of measurement for the magnetic field vector is Tesla (T), which is equivalent to N/A*m (newton per ampere-meter).

4. How does the strength of the magnetic field affect the force on a charged particle?

The strength of the magnetic field directly affects the force on a charged particle. The stronger the magnetic field, the greater the force on the particle. This relationship is described by the formula F = qV * B, where B is the strength of the magnetic field.

5. Can the magnetic field vector be used to determine the velocity of a charged particle?

No, the magnetic field vector alone cannot be used to determine the velocity of a charged particle. The magnetic field vector is dependent on the velocity of the particle, so the velocity must be known in order to calculate the magnetic field vector using F = qV * B.

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