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Soaring Crane

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Four very long, current-carrying wires in the same plane intersect to form a square with side lengths of 42.0 cm , as shown in the figure. The currents running through the wires are 8.0 A, 20.0 A, 10.0 A, and I.

******^

****** |

------10 A------I

-------|--------|-------- 8 A --->

______|_______|

______|_______|

-------|------- |--------- 20 A ---->

10 A point upward; 8A, 20 A to right

Find the magnitude and direction of the current I that will make the magnetic field at the center of the square equal to zero.

I know that I must find the magnetic field at the center of the square due to the wires whose currents are known. Then, the current whose contribution to the magnetic field will exactly cancel the contribution of the other three wires must be found.

Ampere's law must be used, I think, to find B at the center, but how do I apply it? There are more than 1 current, so how do I use it for the 3?

Thank you.

******^

****** |

------10 A------I

-------|--------|-------- 8 A --->

______|_______|

______|_______|

-------|------- |--------- 20 A ---->

10 A point upward; 8A, 20 A to right

Find the magnitude and direction of the current I that will make the magnetic field at the center of the square equal to zero.

I know that I must find the magnetic field at the center of the square due to the wires whose currents are known. Then, the current whose contribution to the magnetic field will exactly cancel the contribution of the other three wires must be found.

Ampere's law must be used, I think, to find B at the center, but how do I apply it? There are more than 1 current, so how do I use it for the 3?

Thank you.

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