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ele401week9

# ele401week9 - inner conducting cylindrical core surround by...

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ELE401 - Field Theory: Tutorial Problems Week 9 1. Magnetic Forces and Torques (In free space μ = μ o ) An infinitely long line of current I 1 = 6 π [A] flows along the z-axis in the + -→ a z direction. Another current I 2 = 2 [A] flows in the triangular circuit ABC in a counter-clockwise direction. The points are A(0,2,2), B(0,6,2) and C(0,6,6) and the current I 2 flows from A to B to C and back to A. (a) Use the expression d -→ F 2 = I 2 dl × -→ B 1 where -→ B 1 is the magnetic flux density vector field due to I 1 , then solve for the force --→ F CA i.e. force on the current clement connecting C to A. (b) Use the expression d -→ T = -→ r × d -→ F 2 to solve for the torque --→ T AB (i.e. on the current element connecting A to B) taken about the origin. (c) Solve for the total force -→ F T = --→ F AB + --→ F BC + --→ F CA (d) Solve for the total torque -→ T T = --→ T AB + --→ T BC + --→ T CA taken about the origin. 2. Magnetic Materials and Bound Currents An Infinitely long coaxial structure, centered on the z-axis consists of an

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Unformatted text preview: inner conducting cylindrical core, surround by two diﬀerent non-current carrying magnetic material sleeves. completing the cylindrical shell. • Region (1): ρ < a ; μ r = 4 carrier current I o in +-→ a z direction. • Region (2): a < ρ < b ; μ r = 2 no free current • Region (3): b < ρ < c ; no free current, but μ r ( ρ ) =-3 ρ + 4 c-b c-b ; (1) the material is non homogeneous. • Region (4): c < ρ < d ; a conductor carrying current I o in the--→ a z direction; μ r = 4. • Region (5): ρ > d ; free space μ = μ o Solve for-→ H , χ m ,-→ M ,-→ J b ,-→ K b , I bs , I bv in all four regions and show that I bs + I bv = 0 for all cases. 1 a b c d 1 2 3 4 5 I o I o Figure 1: Cross Section of Cylindrical Structure 2...
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ele401week9 - inner conducting cylindrical core surround by...

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