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Unformatted text preview: ELE401  Field Theory: Tutorial Problems Week 8 1. An infinitely long line of current Io [A] passes through the point A(6, 0, 5) in the direction, 3ax + 4ay .  Determine the expression for the magnetic intensity vector H at point P (11, 10, 0). z
P(0, 0, z) z=c z' z=b dz'
K = K a 0 y x
Figure 1: A circle of line current 2. Starting with the expression for a circle of line current located on the circle (see Figure 1) x2 + y 2 = a2 at z = z as sensed at a point P (0, 0, z) as:  H = Ia2 2[a2 + (z  z )2 ] 2
3 az [A/m] (1) (a) Convert this into a suitable expression for an incremental ring of   surface current density K Having a width of dz . ( K = K a )  (b) Integrate to solve for the H field due to a solenoid of radius a and extending from z = b to z = c. 1  (c) Show that the H field due to an infinitely long solenoid (i.e. c and b ) becomes,  H = K az [A/m]  3. If J =
Io a2 az (2)  [A/m2 ] in the conductor (see Figure 2), but J = 0 outside.   (a) Solve for H1 inside the conductor, and H2 outside the conductor, using Ampere's Circuital Law and symmetry.   (b) Solve B1 and B2 inside and outside the conductor respectively. (c) Solve for the flux crossing the surface,
a 2 2a; = 0 z L;   B dS .
s = 0 (3)   (d) If A1 and A2 are given for the two regions, inside and outside the conductor respectively:  A1 =  A2 = Io o 2 az [W b/m] 4a2 Io o a 1 ln  az [W b/m]. 2 2 (4) (5)    Confirm that B = A in both regions. (e) Confirm that the flux calculation in (3c) can also be done using: =   A d l . (6) z J Nonmagnetic o everywhere Conductor a
Figure 2: A conductor 2 ...
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 Spring '08
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