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ele401week10

# ele401week10 - N 2 turns carries current I 2 between the...

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ELE401 - Field Theory: Tutorial Problems Week 10 1. Magnetic Boundary Conditions Problem: The boundary between two diﬀerent magnetic materials is given by z - y = 0. Region 1: z - y > 0 has μ 1 = 3 μ o ( μ r 1 = 3) -→ H 1 = ± 125 + 50 2 ² ~a y + ± 50 2 + 25 ² ~a z ³ A m ´ (1) Region 2: z - y < 0, where μ r 2 is unknown, but -→ H 2 = µ 100 3 2 - 50 2 + 25 ! ~a y - µ 100 3 2 + 50 2 - 25 ! ~a z ³ A m ´ (2) Solve for μ r 2 and -→ K the surface current density on the boundary. 2. A hollow cylindrical conductor with a permeability μ = μ o - outer radius “ b ” [m], inner radius “ a ” [m] - carries a uniform current I o in the positive z direction. Find the expression for the internal inductance L int for “ l ” [m] length of this conductor. Suggestions: Use magnetic energy approach where W m = 1 2 L int I 2 o . Use Ampere’s Circuit Law to solve for -→ H . 3. Mutual Inductance Problem: Take μ = μ o everywhere. Current I 1 ﬂows along N 1 strands on the x axis in the - ~a x direction. A triangular loop consisting of
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Unformatted text preview: N 2 turns carries current I 2 between the points A(10,0,4), B(4,0,4), C(10,0,12) and back to A. Determine the expression for “ M ” the mutual inductance between the two circuits. 4. Faraday’s Law Problem: A circular conducting loop of radius “ a ” [m] exists on the z = 0 plane centred on the origin. The loop is immersed in a magnetic ﬁeld-→ B = B o t~a z [T]. Two points on the loop α ( a, + , 0) cyl and β ( a, 2 π, 0) cyl form an inﬁnitesimal gap in the loop. (a) Calculate V emf = V βα =-dψ dt the voltage induced in the loop. (b) Use-→ ∇ ×-→ E =-∂-→ B ∂t and reverse-curl via integration to solve for-→ E = E ( ρ ) ~a φ [V/m]. (c) Solve for V emf = H l-→ E · d ~ l along the loop. (d) Which terminal α or β is positive?...
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