Question

1.) The inner and outer radii of a toroid are 1.50 cm and 3.30 cm. The toroid has 61 turns and carries a current of 2.20 A. What are the strongest and weakest magnetic fields produced by this toroid? (Enter the magnitudes.)

T(strongest):

T(weakest):

2.) The magnitude of the magnetic field at the center of a 23.0-cm-long solenoid with 600.0 turns is 2.10 mT. What is the current in the windings of the solenoid?

Answer 1

r1 = 1.5 cm

r2 = 3.3 cm

N = 61

I = 2.2

Strongest Magnetic field = T(strongest) = (uo*N*I)/(2pi*r1) = (2*10^-7*61*2.2)/0.015 = 1.8 mT

Weakest Magnetic field = T(weakest) = (uo*N*I)/(2pi*r2) = (2*10^-7*61*2.2)/0.033 = 0.81 mT

2) L = 0.23 m

N = 600

n = N/L = 2608.7

B = 2.1 mT

B = uo*n*I ========> I = B/(uo*n) = (2.1*10^-3)/(4pi*10^-7*2608.7) = 640.6 mA