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ele401week5

# ele401week5 - pv iii Q ps Q pv(h V x if V l = 0(i V(0(j W...

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ELE401 - Field Theory: Tutorial Problems Week 5 1. A slab of conducting material with conductivity σ exists in the region: a r b ; π 2 θ π ; π 2 φ π Taking the ~ E -ﬁeld to the ~ E = E o r 2 b a r [ V/m ] solve for the resistance in the r direction between the surfaces r = a and r = b . 2. A piece of dielectric material is held between two conducting planes located at x = 0 and x = l . If the polarization vector ﬁeld inside the dielectric is ~ P = ( ax 2 + b ) c a x [ C/m 2 ] (1) solve for the following if the cross-sectional area of the dielectric slab/rod is taken as “ A ” [ m 2 ]. (a) ~ E (b) ~ D (c) ρ s @ x =0 - (d) ρ s @ x = l + (e) ρ v (f) i. ρ ps @ x =0 + ii. ρ ps @ x = l - iii. ρ pv (g) i. Q ps ii. Q

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Unformatted text preview: pv iii. Q ps + Q pv (h) V ( x ) if V ( l ) = 0 (i) V (0) (j) W E (Method I) (k) W E (Method II) 1 3. Two extensive homogeneous isotropic linear dielectrics meet on the plane z = y ; or z-y = 0 Region I z-y > 0 has ± r 1 = 4 . Region II z-y < 0 has ± r 2 = 3 . 0 and ~ E 2 = 5 c a x-2 c a y + 4 b a z [ V/m ] If there is no surface charge density on the boundary between the two dielectric. Solve for: (a) ~ E 1 (b) ~ P 1 (c) ~ P 2 (d) ρ ps 1 (e) ρ ps 2 Hint: Take ~ a n = b a z-b a y √ 2 2...
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ele401week5 - pv iii Q ps Q pv(h V x if V l = 0(i V(0(j W...

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