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5. Imagine you have a conductor (think an infinite wire along the z-axis) with a steady electric current I moving in the positive z-direction. The steady current produces a magnetic field B(x, y, z) = B1(x, y, z)i + B2(x, y, z)j + B3(x, y, z)k. Let C be any closed curve that encloses the wire. Then Ampere's Law states that that the circulation of the magnetic field around C is proportional to the current I. Let's denote the constant of proportionality by a. Let C be any circle in the plane z = k centered at the wire. It is known that the magnetic field B has constant magnitude along C and is tangent to the circle C. Find the ||B(1, 2, 3)||. Remark: Ignore units throughout this problem. Also keep in mind that your final answer will be in terms of I and a. 5. Imagine you have a conductor (think an infinite wire along the z-axis) with a steady electric current I moving in the positive z-direction. The steady current produces a magnetic field B(x, y, z) = B1(x, y, z)i + B2(x, y, z)j + B3(x, y, z)k. Let C be any closed curve that encloses the wire. Then Ampere's Law states that that the circulation of the magnetic field around C is proportional to the current I. Let's denote the constant of proportionality by a. Let C be any circle in the plane z = k centered at the wire. It is known that the magnetic field B has constant magnitude along C and is tangent to the circle C. Find the ||B(1, 2, 3)||. Remark: Ignore units throughout this problem. Also keep in mind that your final answer will be in terms of I and a

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