Hello, I am stuck on the practice problem. I'm not sure I am doing it right. Could you help guide me through these steps? A cylindrical conductor wire in free space has a radius of a = 5 cm. It is placed on z axis. It carries a steady current and therefore produces a magnetic field. Suppose the magnetic field in the wire is characterized by H = phiˆ 2/r [1-(4r + 1)e^(4r) ] (A/m), r < a Use two approaches to find the total current I through the wire. One approach is by the integral form of Ampere’s law. The second approach is by the differential form to find the current density J and then the total current I. Thank you for your time and help.

Hello, I am stuck on the practice problem. I'm not sure I am doing it right. Could you help guide me through these steps? A cylindrical conductor wire in free space has a radius of a = 5 cm. It is placed on z axis. It carries a steady current and therefore produces a magnetic field. Suppose the magnetic field in the wire is characterized by H = phiˆ 2/r [1-(4r + 1)e^(4r) ] (A/m), r < a Use two approaches to find the total current I through the wire. One approach is by the integral form of Ampere’s law. The second approach is by the differential form to find the current density J and then the total current I. Thank you for your time and help.

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Hello, I am stuck on the practice problem. I'm not sure I am doing it right. Could you help guide me through these steps?

A cylindrical conductor wire in free space has a radius of a = 5 cm. It is placed on z axis. It carries a steady current and therefore produces a magnetic field. Suppose the magnetic field in the wire is characterized by

H = phiˆ 2/r [1-(4r + 1)e^(4r) ] (A/m), r < a

Use two approaches to find the total current I through the wire. One approach is by the integral form of Ampere’s law. The second approach is by the differential form to find the current density J and then the total current I.

Thank you for your time and help.

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Step 1: Given data and to find:

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Step 2: 1st approach using integral form of ampere's law

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Step 3: 2nd approach using differential form to first find current density

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Step 4: Here total current calculated by integrating current density over dA

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