Question

A toroid is effectively a solenoid that curls in on itself. Consider a toroid of inner radius a and outer radius b, consisting of N turns of wire total, as shown below. Throughout the following problems, let r describe a distance measured from the center of the toroid, and let I describe the current being carried in the wire of the toroid. 1. Use Ampère’s Law to show that the magnetic field inside the body of the toroid is zero (in other words, B = 0 for r < a). 2. Use Ampère’s Law to show that the magnetic field outside the toroid is also zero (in other words, B = 0 for r > b). 3. Use Ampère’s Law to show that the magnetic field inside the volume of the toroid (a < r < b) is given by the following relationship: B_toroid = (??IN) / (2?r) (where I_enclosed = NI)

          A toroid is effectively a solenoid that curls in on itself. Consider a toroid of inner radius a and outer radius b, consisting of N turns of wire total, as shown below.

Throughout the following problems, let r describe a distance measured from the center of the toroid, and let I describe the current being carried in the wire of the toroid.

1. Use Ampère’s Law to show that the magnetic field inside the body of the toroid is zero (in other words, B = 0 for r < a).
2. Use Ampère’s Law to show that the magnetic field outside the toroid is also zero (in other words, B = 0 for r > b).
3. Use Ampère’s Law to show that the magnetic field inside the volume of the toroid (a < r < b) is given by the following relationship: B_toroid = (??IN) / (2?r)
(where I_enclosed = NI)

A toroid is effectively a solenoid that curls in on itself. Consider a toroid of inner radius a and outer radius b, consisting of N turns of wire total, as shown below.

Throughout the following problems, let r describe a distance measured from the center of the toroid, and let I describe the current being carried in the wire of the toroid.

1. Use Ampère’s Law to show that the magnetic field inside the body of the toroid is zero (in other words, B = 0 for r < a).
2. Use Ampère’s Law to show that the magnetic field outside the toroid is also zero (in other words, B = 0 for r > b).
3. Use Ampère’s Law to show that the magnetic field inside the volume of the toroid (a < r < b) is given by the following relationship: Btoroid = (??IN) / (2?r)
(where Ienclosed = NI)

Added by Manuel E.

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