Find the magnetic field at the center

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SUMMARY

The magnetic field at the center of a half-circle wire carrying a current of 7A with a radius of 0.2m is calculated using the formula B = (μ0 I)/(2R) multiplied by 0.5. The correct calculation yields a magnetic field strength of 11μT, confirming option A as the correct answer. The initial mistake involved using the formula for a straight wire instead of the appropriate formula for a curved wire segment.

PREREQUISITES
  • Understanding of magnetic fields and their calculations
  • Familiarity with the Biot-Savart Law
  • Knowledge of the permeability of free space (μ0)
  • Basic algebra for manipulating equations
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Fatima Hasan
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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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The formua for B that you used is for a straight wire. This wire is not straight.
 
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 ?
 
What is ##\theta## in your formula?
 
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:

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