Download ECT1026 Tutorial 3B_Question

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
2R
(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
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