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Let bbe a constant. Prove that the equation of the plane y=bisr=bcscφcscθin spherical coordinates.

Short Answer

Expert verified

This is proved using relationx=rsinϕcosθ,y=rsinϕsinθ,z=rcosϕ.

Step by step solution

01

Given Information

Equation of rectangular coordinates is given as y=b (bis constant).

02

Simpification

We know that

x=rsinϕcosθ,y=rsinϕsinθ,z=rcosϕ

For conversion of given equation of plane to spherical coordinates, use y=rsinϕsinθin given equation

rsinϕsinθ=b

r=bsinϕsinθ

=b1sinϕ1sinθ

role="math" localid="1652391295106" r=bcscϕcscθ

Hence proved.

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