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ECT1026 Field Theory MMU/FOE/2007/08 Tutorial 3 Magnetostatic – Part B Faraday’s Law Q4. The field coils of a 6-pole dc generator each having 500 turns, are connected in series. When the field is excited, there is a magnetic flux of 0.02 Wb/pole. If the field circuit is opened in 0.02 second and residual magnetism is 0.002 Wb/pole, calculate the average voltage induced across the field terminals. Q5. The rectangular loop in Fig. 3-1 is coplanar with a long straight wire carrying a current I(t) = 2.5 cos(2 × 10 4 t) (A). (a) Determine the emf induced across a small gap created in the loop. (b) Determine the magnitude of the current that would flow through a 4 resistor connected across the gap. The loop has an internal resistance of 1 . z r1=5cm I (t) =2.5 cos(2×10-4)t l=10cm r2=15cm Fig-3-1 R Induction Calculation and Magnetic Energy Q6. Show that the total inductance of a coaxial conductor with inner conductor radius of a, and outer conductor radius of b, as shown in Fig. 3-2, is given by: L ol ol b ln 8 2 a 1 ECT1026 Field Theory MMU/FOE/2007/08 Fig. 3-2 Q7. A copper wire of radius R carries a steady current I. The magnetic flux density at Ir a distance r from its axis is given by, B o 2 (for r < R). Find 2R (a) The magnetic energy density at a distance r from the axis (for r < R). (b) The total magnetic energy within a cylindrical shell of length l and radius r surrounding the wire. (c) The inductance per unit length. Self-Inductance and Mutual Inductance Q8. The self-inductance of a coil of 500 turns is 0.25H. If 60% of the flux is linked with a second coil of 10000 turns, calculate the mutual inductance of the two coils and find the emf induced in the second coil when current in the first coil changes at the rate of 100 A/s. Q9. In terms of dc current I, how much magnetic energy is stored in the insulating medium of a 2 m long air-filled section of a coaxial transmission line, given that the radius of the inner conductor is 5 cm and the inner radius of the outer conductor is 10 cm? Magnetic Boundary Conditions Q10. Assume that no surface current exist at the parallel interfaces shown in Fig. 3-3. Prove that the relationship between 4 and 1 is independent of 2 . 2 ECT1026 Field Theory MMU/FOE/2007/08 3 4 2 2 1 B3 3 B2 1 B1 Fig. 3-3 3