Question

3. Toroid a) A toroid is formed by winding a wire which carries current I with N turns. The toroid has a mean radius R, and a cross-section radius rc which is smaller than R. Using Ampere’s law, derive an expression for B inside the toroid as the function of radial distance r which is the distance from the center of the toroid. Again, draw a figure with an amperian loop, direction of the path, and the direction of the magnetic field. Toroid R = mean radius rc = cross-section radius N = 2000, I = 2 A, R = 20 cm, rc = 6 cm for part b) and c) b) Inside the toroid is filled with annealed iron with ?m = 5500. Find the magnitude of the magnetization at r = R. c) Find the magnitude of the total magnetic field at r = R + rc/2 of the annealed iron filled toroid.

          3. Toroid
a) A toroid is formed by winding a wire which carries current I with N turns. The toroid has a mean radius R, and a cross-section radius rc which is smaller than R. Using Ampere’s law, derive an expression for B inside the toroid as the function of radial distance r which is the distance from the center of the toroid. Again, draw a figure with an amperian loop, direction of the path, and the direction of the magnetic field.

Toroid
R = mean radius
rc = cross-section radius

N = 2000, I = 2 A, R = 20 cm, rc = 6 cm for part b) and c)

b) Inside the toroid is filled with annealed iron with ?m = 5500. Find the magnitude of the magnetization at r = R.

c) Find the magnitude of the total magnetic field at r = R + rc/2 of the annealed iron filled toroid.

3. Toroid
a) A toroid is formed by winding a wire which carries current I with N turns. The toroid has a mean radius R, and a cross-section radius rc which is smaller than R. Using Ampere’s law, derive an expression for B inside the toroid as the function of radial distance r which is the distance from the center of the toroid. Again, draw a figure with an amperian loop, direction of the path, and the direction of the magnetic field.

Toroid
R = mean radius
rc = cross-section radius

N = 2000, I = 2 A, R = 20 cm, rc = 6 cm for part b) and c)

b) Inside the toroid is filled with annealed iron with ?m = 5500. Find the magnitude of the magnetization at r = R.

c) Find the magnitude of the total magnetic field at r = R + rc/2 of the annealed iron filled toroid.

Added by Andrew H.

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