Question

A21921 Section B 4. (a) Sketch the lines of magnetic flux B inside and outside a long, curent- carrying solenoid, labelling a clearly the direction of B relative to the direction of current flow. all of the important tures, and indicating Stating any approximations that you make, show that the axial magnetic [5 fux density, B, deep inside a long solenoid of length 1, total number of turns N, carrying a current 1, is approximately Two solenoids are arranged as shown in Figure 4, with the smaller solenoid placed on the axis of, and deep inside, a much larger solenoid. The large solenoid has a total number of turns Ni, of 10000, a length li of 10 cm and a radius ri of 1 cm. The smaller solenoid has a total number of turns N2, of 3000, a length l of 3 cm and a radius of r2 0.3 cm. The large, outer solenoid carries a peak current I of 0.01 A at frequency f-10 kHz large solenoid small solenoid axis Figure 4 Find the peak value of axial magnetic flux density within the solenoids. 1 (i) By considering the total flux linkage of the smaller solenoid due to the [4] current flowing in the larger solenoid, find the mutual inductance between them (ili) Calculate the peak voltage developed across the smaller solenoid, and [3] comment on the phase difference between this voltage and the current in the larger solenoid. (iv) The induced voltage, generated by the larger solenoid, causes a current 4 of 5 mA to flow in the turns of the smaller solenoid. Calculate the magnetic energy density along the central axis of the smaller solenoid.

Answer 1

(1-0) ,σ R90) (8-q0) 2 3000 2 -1 10 cm 10X(0 om 2 2 0-3 cm 2. 11ニ0.01 A Hon 나 = ути о7x ¡oooox o.oi L1 l0 4- dt

BIA 2 0.01 x 10 -10 212 2. 10 91 (a y