In the figure, part of a long insulated wire carrying current i = 9.19 mA is ben
ID: 1450616 • Letter: I
Question
In the figure, part of a long insulated wire carrying current i = 9.19 mA is bent into a circular section of radius R = 1.71 cm. What are the x-component, the y-component, and the z-component of the magnetic field at the center of curvature C if the circular section lies in the plane of the page as shown? What are the x-component, the y-component, and the z-component of the magnetic field at the center of curvature C if the circular section is perpendicular to the plane of the page after being rotated 90 degree counterclockwise as indicated?Explanation / Answer
Magnetic field at the centre of a current carrying ring, B = 2pikI/d
Magnetic field due to a long current carrying wire, B = 2kI/d
1. x-component = 0
2. y-component = 0
3. From right hand rule, we have that the field is only along z axis
B = 2*pi*k*I/R + 2kI/R = 2*3.14*10^-7 *9.19*10^-3 / 1.71*10^-2 + 2*10^-7*9.19*10^-3/1.71*10^-2 = [3.375 + 1.0748]*10^-7 T = 4.449*10^-7 T [out of the paper]
4. for case 2
B due to long wire = 3.375*10^-7 T [out of paper
B due to loop = 1.0748*10^-7 T [along +ve x axis]
x component = 1.0748*10^-7 T
5. y component = 0
6. z component = 3.375*10^-7 T [out of paper]
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