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ele401week4

# ele401week4 - o< ρ< a and carries a volume charge...

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ELE401 - Field Theory: Tutorial Problems Week 4 1. A short line of line-charge density ρ L exist on the z-axis between z = b and z = a , ( b > a > 0). (a) Solve for V ( ~ r ) at a general point P ( ρ,φ,z ) using: V ( ~ r ) = Z L 0 ρ L dl 0 4 πε o | ~ r - ~ r 0 | (1) (b) Use ~ E = - ~ V to solve for the ~ E ﬁeld at a general point P ( ρ,φ,z ). (N.B.: This approach is easier than using Coulomb’s law directly.) Figure 1: Two concentric cylinders 1

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2. Two concentric cylinders are centred on the z-axis is shown in Figure 1. The cylinders are inﬁnitely long, but the problem will focus on an “ l ” [ m ] length of cylinder only. The inner cylinder is solid (
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Unformatted text preview: o < ρ < a ) and carries a volume charge density ρ v where ρ v is : ρ v = α πa 2 [ C/m 3 ] (2) The outer cylinder at ρ = b is a thin shell which carries a surface charge density ρ S such that: ρ S =-α 2 πb [ C/m 2 ] (3) (a) Solve for ~ E every where. (b) Solve for V ( ~ r ) every where, if V ( b ) = 0. (c) Solve for energy in the “ l ” [ m ] length using: i. 1 2 R v ρ v V dv + 1 2 R S ρ S V dS ii. 1 2 R v ~ D · ~ Edv 2...
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ele401week4 - o< ρ< a and carries a volume charge...

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