A toroid has an average radius of 14 cm and a cross-sectional area of 3 cm 2 . I
ID: 2011808 • Letter: A
Question
A toroid has an average radius of 14 cm and a cross-sectional area of 3 cm2. It is wound with fine wire, 69 turns/cm measured along its mean circumference, and the wire carries a current of 3 A. The core is filled with a paramagnetic material of magnetic susceptibility 3 *10-4.
(a) What is the magnitude of the magnetic field within the substance?
T
(b) What is the magnitude of the magnetization?
A/m
(c) What would the percentage difference in the magnitude of the magnetic field be if there were no paramagnetic core present?
%
Explanation / Answer
Given: Average radious of the toroid = r = 14 cm = 0.14 m Area of the cross-section = A= 3 cm2 = 3 x10-4 m2 current carrying in the wire = I = 3A No. of turns opffered by the toroid = N = 69 /cm = 6900 /m paramagnetic material of magnetic susceptibility = = 3 x 10-4 (a) Thus, Magnetic field due to toroid is given by the formual as : B = o N I / 2 r = 4x10-7 (6900)(3) / 2(0.14) = 295714.28 x10-7T = 0.029571428 T (b) Let I be the Intensity of Magnetiazation we have a relation between the B and I as = I / B or I = B = ( 3 x 10-4 )(0.029571428 ) = 0.08871428x 10-4 A/m (c) if there were no paramagnetic core present I wil be 0 , thus 0 % of difference in the magnitude of the magnetic field is produced(c) if there were no paramagnetic core present I wil be 0 , thus 0 % of difference in the magnitude of the magnetic field is produced
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