Calculating Magnetic Field Using Biot-Savart Law for Concentric Arcs

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In summary, the problem involves finding the magnitude of the magnetic field at point P in a closed loop with a counterclockwise current of 6.90 A. The loop has an outer arc with a radius of 65.0 cm and an inner arc with a radius of 41.0 cm. The solution requires splitting the question into 4 parts and using the cross product to simplify calculations. The relevant equation is db=\frac{uI dl x r}{4\pi r^3} where dl and r are vectors and x represents the cross product.
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Winzer
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Homework Statement


The closed loop shown in the figure below carries a current of 6.90 A in the counterclockwise direction. The radius of the outer arc is 65.0 cm, that of the inner arc is 41.0 cm. Find the magnitude of the magnetic field at point P if the angle 60 deg.

Homework Equations


Savart
[tex] db=\frac{uI dl x r}{4\pi r^3}[/tex]
dl and r are vectors
x means cross product

The Attempt at a Solution


Basically integrate the outer wire, the inner wire and add them up right?
 

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  • #2
You will have to split the question into 4 parts to find the contribution of the 4 different sections. The cross product is useful here as it simplifies the different parts greatly.
 
  • #3
I figured it out.
 

Related to Calculating Magnetic Field Using Biot-Savart Law for Concentric Arcs

1. What is the Biot Savart law?

The Biot Savart law is a mathematical equation that describes the magnetic field produced by a steady current in a conductive material. It is named after the scientists Jean-Baptiste Biot and Felix Savart, who first described the relationship between current and magnetic field in the early 19th century.

2. How are concentric arcs related to the Biot Savart law?

Concentric arcs are a graphical representation of the magnetic field produced by a current-carrying wire, according to the Biot Savart law. The arcs represent the direction and strength of the magnetic field at different distances from the wire.

3. What factors affect the strength of the magnetic field in concentric arcs?

The strength of the magnetic field in concentric arcs is affected by the distance from the current-carrying wire, the current magnitude, and the material properties of the wire. The Biot Savart law also takes into account the angle between the wire and the point at which the field is being measured.

4. How are concentric arcs used in practical applications?

Concentric arcs have many practical applications, such as in the design of electromagnets and in the construction of motors and generators. They are also used in medical imaging techniques, such as MRI machines, which use magnetic fields to produce detailed images of the body's internal structures.

5. Are there any limitations to the Biot Savart law and concentric arcs?

While the Biot Savart law and concentric arcs provide accurate predictions for simple current-carrying wires, they may not be applicable to more complex systems. In addition, they do not account for non-steady currents or magnetic materials, and may not accurately predict the behavior of magnetic fields at very small scales.

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