What is B = (mu * l)/(2pi*r) used for?

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In summary, the equation B=(mu*l)/(2*pI*r) is used to find the magnetic field due to a straight wire with a current. It is derived from Ampere's law and can also be derived from Biot-Savart's law. The equation suggests that the magnetic field is the same at any point on the same circle, with the strength of the field increasing with the strength of the current and decreasing with the distance from the wire. More information can be found at the provided link."
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alice emily
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Homework Statement



what is this equation used for

Homework Equations



B=(mu*l)/(2*pI*r)

The Attempt at a Solution

 
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It's ampere's law applied to a straight wire. (I think you can also derive it from Biot savart)

Its used to find the magnetic field due to a straight wire w/current.

Picture a bunch of circles, each one centered on the wire. The equation says that the magnetic field is the same at any point on the same circle. Also, the farther the cirlce is, the weaker the magnetic field and the stronger the current, the stronger the magnetic field.
 

FAQ: What is B = (mu * l)/(2pi*r) used for?

What is the purpose of the equation B = (mu * l)/(2pi*r)?

The equation B = (mu * l)/(2pi*r) is known as the Biot-Savart Law and is used to calculate the magnetic field strength at a given point due to a current-carrying wire or a straight conductor. It is commonly used in the study of electromagnetism and plays a crucial role in understanding the behavior of magnetic fields.

How is the equation B = (mu * l)/(2pi*r) derived?

The Biot-Savart Law was derived by French physicists Jean-Baptiste Biot and Félix Savart in the early 19th century. They conducted experiments to investigate the relationship between the magnetic field strength and the current-carrying wire and found that it is directly proportional to the current and inversely proportional to the distance from the wire, which led to the formulation of this equation.

What are the units of measurement for the variables in the equation B = (mu * l)/(2pi*r)?

The units of measurement for the variables in this equation are as follows:

  • B (magnetic field strength) - Tesla (T)
  • mu (magnetic permeability) - Henry per meter (H/m)
  • l (length of the conductor) - meter (m)
  • r (distance from the wire) - meter (m)

Can the equation B = (mu * l)/(2pi*r) be used for any type of current-carrying wire?

Yes, the Biot-Savart Law can be used for any type of current-carrying wire, as long as the wire is straight and the current is constant. It is valid for both DC and AC currents and is a fundamental law in electromagnetism.

In what real-world applications is the equation B = (mu * l)/(2pi*r) commonly used?

The Biot-Savart Law has many practical applications, including in the design of electric motors, generators, and transformers. It is also used in the study of magnetic materials and their properties. Additionally, it is used in medical imaging techniques such as magnetic resonance imaging (MRI) and in navigation systems using magnets, such as compasses and magnetic levitation trains.

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