Component form of magnetic field

In summary, when a 2.0 m long wire carrying a current of 8.2 A is placed within a uniform magnetic field B, a magnetic force of (-2.2 j)N acts on the wire when it is along the +x axis and a force of (2.2 i -4.2k)N acts on the wire when it is along the +y axis. The direction of the B-field in the y direction is 0, but it is unknown in the x and z directions. To find the direction, the equation F=ILBsin(theta) can be used with the dot product. By imagining the vector arrows for the force and magnetic field and finding the cross product, the direction of
  • #1
mgoff87
4
0
A 2.0 m long wire carries a current of 8.2 A and is immersed within a uniform magnetic field B.
When this wire lies along the +x axis, a magnetic force F= (-2.2 j)N acts on the wire, and when it lies on the +y axis, the force is F = (2.2 i -4.2k)N.

I saw through inspection that B in the y direction is 0, but I'm having difficulties with the x and z direction.

I know the equation in F=ILBsin(theta) and that i might need to use a dot product, but I'm stuck after that...
 
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  • #2
The force generated from a magnetic field is in the direction of the cross product of the current and the magnetic field itself. Remembering that you should easily be able to figure ot the direction of the B-field in these two cases separately, do some vector work and get the answer. I think it helps to imagine the vector arrows for the force and magnetic field, and then imagine a vector arrow perpendicular to both of those to see what you have to calculate.
 
  • #3
I figured it out...all i needed to do was set it up as a matrix and find the determinate(ie the cross product) and everything worked out fine!
 

Related to Component form of magnetic field

1. What is the component form of magnetic field?

The component form of magnetic field is a mathematical representation that breaks down the magnetic field into its individual components, typically denoted as Bx, By, and Bz. These components represent the strength and direction of the magnetic field in each respective axis (x, y, and z).

2. How is the component form of magnetic field calculated?

The component form of magnetic field is calculated using vector calculus, specifically the cross product of the magnetic field vector and the unit vectors of each axis. This results in three equations for Bx, By, and Bz, which can then be solved to determine the components of the magnetic field.

3. Why is the component form of magnetic field important?

The component form of magnetic field is important because it allows scientists to understand and analyze the magnetic field in a more detailed and precise manner. By breaking down the field into its components, we can better understand how it interacts with other forces and how it affects objects in its vicinity.

4. How does the component form of magnetic field relate to other forms of magnetic field representation?

The component form of magnetic field is one of several ways to represent the magnetic field. It is closely related to the vector form of magnetic field, which uses a single vector to represent the magnitude and direction of the field. The component form is also related to the scalar form, which uses a single value to represent the strength of the field.

5. Can the component form of magnetic field change over time?

Yes, the component form of magnetic field can change over time. This is because magnetic fields are dynamic and can be influenced by various factors such as the movement of charged particles or the presence of other magnetic fields. In order to fully understand the behavior of a magnetic field, it is important to consider how its components may change over time.

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