Answer :
Final answer:
The magnetic field inside a toroid is calculated using the formula B = μ0nI, the magnetic field in this instance comes out to be 2.6 x 10^-3 T or 2.6 mT.
Explanation:
The question here is related to the magnetic field inside a toroid.
The formula to find the magnetic field inside a toroid is B = μ0nI, where B is the magnetic field, μ0 is the magnetic constant, n is the number of turns per unit length, and I is the current.
In this case, the radius difference is 1 cm, which is the diameter of the cross-section of the coil, and the mean radius of the toroid is (28+29)/2 = 28.5 cm. The total length of the coil would be its circumference which equals 2*pi*r = 2*pi*28.5 cm = 179 cm. The number of turns per unit length then calculates to be 3700 turns/179 cm = ~20.67 turns/cm.
Substituting the known values from the problem into the equation, B = (4*pi*10^-7 T.m/A)(20.67 turns/cm)(10 A), the magnetic field will be 2.6 x 10^-3 T or 2.6 mT.
The formula and calculations above shows how we can find the magnetic field inside a toroid given the inner and outer radius of the toroid, the number of wire turns, and the amount of current running through the wire.
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