Problem 358 find the laplacian of the following

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Unformatted text preview: ∂ 0 0 − (sin φ ) + φ r ∂φ ∂z ∂z ∂r ∂ 1∂ ˆ (r cos φ ) (r(sin φ )) − +z r ∂r ∂φ 1 1 ˆ ˆ ˆ ˆ = r0 + φ 0 + z (sin φ + (r sin φ )) = z sin φ 1 + , r r π 2 1 ˆ ˆ ∇×B · d s = · (zr dr d φ ) z sin φ 1 + r φ =0 r =0 ˆ =r π = 2 φ =0 r =0 sin φ (r + 1) dr d φ = − cos φ ( 1 r2 + r) 2 2 r =0 π φ =0 = 8. Problem 3.58 Find the Laplacian of the following scalar functions: (a) V1 = 10r3 sin 2φ (b) V2 = (2/R2 ) cos θ sin φ Solution: (a) 1∂ ∂ V1 1 ∂ 2V1 ∂ 2V +2 r +2 r ∂r ∂r r ∂φ2 ∂z 1 ∂2 ∂ 1∂ (10r3 sin 2φ...
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This homework help was uploaded on 02/20/2014 for the course EEC 130 at UC Davis.

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