Find the magnetic field at the center

In summary, the correct formula for finding the magnetic field of a wire shaped as a half circle is B = (μ0*I*θ)/(2R), where θ is the angle of the half circle. Using this formula, the magnetic field at the center of the wire with current I=7A and radius R=0.2m is 11μT. The mistake in the attempt at a solution was using the formula for a straight wire instead of accounting for the curvature of the wire.
  • #1
Fatima Hasan
319
14

Homework Statement


A wire carrying current I=7A is shaped as half circle of radius R=0.2m.The magnetic field B(in μT) at the center is :
A)11.0(k)
B)7.9(k)
C)9.4(k)
D)6.3(k)
E)4.0(-k)

Homework Equations


B=(μ0 I)/(2πR)

The Attempt at a Solution


B = (4π*10-7 *7)/(0.2*2*π) * 0.5 (Multiply by 1/2 because the wire is shaped as half circle).
B = 3.5*10-6 T = 3.5μT
Could anyone tell me where is my mistake?
 
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  • #2
The formua for B that you used is for a straight wire. This wire is not straight.
 
  • #3
Gene Naden said:
The formua for B that you used is for a straight wire. This wire is not straight.
B = (μ*I)/(4*π*r) *θ ?
 
  • #4
What is ##\theta## in your formula?
 
  • #5
Gene Naden said:
What is ##\theta## in your formula?
B = (μ*I)/(2R) *0.5
= ( 4*10-7π *7)/(2*0.2) *0.5
= 10.99μT
=11 μT
 
Last edited:

1. What does it mean to find the magnetic field at the center?

When we talk about finding the magnetic field at the center, we are referring to calculating the strength and direction of the magnetic field at the exact center point of a magnetic field source, such as a magnet or an electromagnet.

2. How is the magnetic field at the center calculated?

The magnetic field at the center is calculated using the principles of electromagnetism. It involves determining the strength and direction of the magnetic field lines at various points around the magnetic field source and using mathematical equations to find the resulting field at the center.

3. What factors affect the magnetic field at the center?

The strength and direction of the magnetic field at the center can be affected by various factors such as the strength of the magnetic field source, the distance from the source to the center point, and the orientation of the source. Additionally, the presence of other magnetic fields or materials can also impact the resulting field at the center.

4. Why is it important to find the magnetic field at the center?

Knowing the magnetic field at the center is important in understanding the behavior and interactions of magnetic fields. It can also be useful in designing and optimizing magnetic devices, such as motors and generators, as well as in various scientific and technological applications.

5. What are some methods used to find the magnetic field at the center?

There are several methods used to find the magnetic field at the center, including using mathematical equations based on the principles of electromagnetism, using special equipment such as a Gaussmeter or a magnetometer, and performing experiments to measure the effects of the magnetic field at the center point.

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