ele401week3

# ele401week3 - ELE401 Field Theory Tutorial Problems Week 3...

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ELE401 - Field Theory: Tutorial Problems Week 3 1. From ﬁrst principles using d ~ E = dQ ( ~ r - ~ r 0 ) 4 πε o | ~ r - ~ r 0 | 3 . (a) Develop the ~ E -ﬁeld expression for the quarter circle of line charge density as shown on the ﬁgure 1. The ~ E -ﬁeld to be found at point P (0 , 0 ,z ). x y z P(0,0,z) z' a ρ L [C/m] Figure 1: Quarter circle of line charge density (b) Solve 1(a) for the case where the line charge forms a complete circle (i.e. φ : 0 2 π ). (c) Drop the circle of line charge down onto the x-y plane by letting z 0 0. 2. (a) Use the expression derived in 1(c) to develop the incremental expres- sion for a narrow circular strip of surface charge ρ s as shown on the ﬁgure 2. Then use the new expression for d ~ E to solve for a disk or washer shape surface of charge such that a ρ b . (b) Let a 0, then ... 1

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x y z P(0,0,z) a ρ s [C/m] 2 ρ ' d' ρ b Figure 2: A narrow circular strip of surface charge ρ s .
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ele401week3 - ELE401 Field Theory Tutorial Problems Week 3...

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