Solving a Biot-Savart Problem: Idx, r and dB

In summary, The problem at hand involves finding the magnetic flux densities at a given point using the Biot-Savart law. The only difficulty mentioned is understanding what Idx represents and whether it is an infinite wire or a point. The method of solving involves substituting Idx for Idl and taking the cross product with r. It is uncertain whether integration is necessary to find B.
  • #1
ermines
45
0
i personally think that this is just a very simple problem since the problem only requires plugging the right values into the formula. I'm just having trouble with one minor detail.

Homework Statement



For the current element Idx(ax+ay) A situated at P(1,-2,2), find the magnetic flux densities at P(2,-1,3).

Homework Equations



Biot-Savart

dB = (K)(IdI x r)/rr

The Attempt at a Solution



my only problem in here is that I'm having a hard time figuring out what idx is? do i just substitute it for Idl then just get its cross product with r and so on? also, do i need to actually integrate it to get B?

that is all and thanks.
 
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  • #2
What is Idx(ax+ay) ?
What kind of current element do we have here ? Wire, infinite wire, semi infinite wire ?

marlon
 
  • #3
hmmm...never thought of that question, marlon...

i suppose that it is an infinite wire? or can't it just be just a point with such property? will it actually make a difference?
 

1. What is a Biot-Savart problem?

A Biot-Savart problem is a physics problem that involves calculating the magnetic field generated by a current-carrying wire or a moving charged particle. It is named after the scientists Jean-Baptiste Biot and Félix Savart who first described the relationship between current and magnetic field in the early 19th century.

2. What are the variables involved in solving a Biot-Savart problem?

The variables involved in solving a Biot-Savart problem are the current (I), the distance from the wire or particle (r), and the differential magnetic field (dB) at that distance. These variables are typically represented by the equation dB = μ0I(dl x r)/4πr^3, where μ0 is the permeability of free space and dl is the length element of the wire or the path of the charged particle.

3. How do you calculate Idx, r, and dB in a Biot-Savart problem?

To calculate Idx, r, and dB, you will need to first identify the current (I) and the distance (r) from the wire or particle to the point where you want to calculate the magnetic field. Next, you will need to determine the length element (dl) of the wire or the path of the charged particle. Once you have these values, you can plug them into the equation dB = μ0I(dl x r)/4πr^3 to calculate the differential magnetic field (dB).

4. Can the Biot-Savart law be applied to any current-carrying wire or moving charged particle?

Yes, the Biot-Savart law can be applied to any current-carrying wire or moving charged particle, as long as the current is steady and the motion of the particle is constant. It can also be applied to a combination of multiple wires or particles, as long as the individual contributions are calculated and then summed together.

5. What are some real-life applications of the Biot-Savart law?

The Biot-Savart law has many real-life applications, including in the design of electromagnets, motors, and generators. It is also used in the study of Earth's magnetic field and in medical imaging techniques such as magnetic resonance imaging (MRI). In addition, the Biot-Savart law is used in the field of aeronautics for calculating the magnetic field around an aircraft and in navigation systems using magnetometers.

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