Calculating Magnetic Field at Center of Circular Arc | Loop Current Bending

In summary, the magnetic field, B, at the center of a circular current loop with radius r and current I is given by the Biot-Savart law. In the case of a long straight wire bent at a 90 degree angle in a circular arc of radius r, the magnetic field at the center of the arc P can be calculated by adding the magnetic field generated by the whole circle and the magnetic field generated by the arc section, which is \frac{1}{4}\frac{\mu I}{2r}.
  • #1
frozen7
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iv)The magnetic field, B at the center of a circular current loop of radius r carrying current I, is given by the expression . If one of the long straight wires is bent 90o in a circular arc of radius r (refer to Figure B1). What is the magnetic field at the center of the arc P?

Can anyone help me? Help needed.
 

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  • #2
Please show what you've tried.

Use the Biot-Savart law.
 
  • #3
What i know is for the arc section, the magnetic field should be (miu)I / 2r and for the straight wire is (miu)I / 2(pie)r. I don't know how to start this question. Should I just sum up both magnetic field?
 
  • #4
Using the superposition principle, yes you may add them together. The [tex]\frac{\mu I}{2r}[/tex] seems to be the magnetic field generated by a whole circle. Thus the field generated by the arc in the picture is [tex]\frac{1}{4}\frac{\mu I}{2r}[/tex].

EDIT: Replied the same minute :smile:.
 

FAQ: Calculating Magnetic Field at Center of Circular Arc | Loop Current Bending

How do you calculate the magnetic field at the center of a circular arc?

To calculate the magnetic field at the center of a circular arc, you can use the formula B = μ₀I/2R, where B is the magnetic field strength, μ₀ is the permeability of free space, I is the current flowing through the arc, and R is the radius of the arc.

What is the significance of the loop current in calculating the magnetic field?

The loop current is the current flowing through the circular arc. It is significant because it is the source of the magnetic field and determines its strength at the center of the arc.

How does the bending of the loop current affect the magnetic field at the center of the arc?

The bending of the loop current can change the direction and strength of the magnetic field at the center of the arc. The closer the current is to the center, the stronger the magnetic field will be. Additionally, the direction of the current will determine the direction of the magnetic field.

Are there any other factors that can affect the calculation of the magnetic field at the center of a circular arc?

Yes, there are other factors that can affect the calculation of the magnetic field at the center of a circular arc. These can include the material the arc is made of, the presence of other nearby magnetic fields, and the shape and orientation of the arc.

Can this formula be applied to other shapes besides a circular arc?

Yes, this formula can be applied to other shapes besides a circular arc as long as the current is flowing in a loop. Some examples include a square loop, a rectangular loop, or a triangular loop.

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