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sineoko [7]
3 years ago
6

Compute the electric charge on the surface which is the portion of the cone z = 3x2 + 3y2 in the first octant that lies between

the planes z = 2 and z = 6. The charge density on the surface is given by σ(x, y, z) = xyz2 coulombs per square meter.
Physics
1 answer:
dsp733 years ago
5 0

Answer:

9828 coulombs

Explanation:

z = \sqrt{3x^2 + 3y^2}

Relation between the cartesian and polar coordinates

x = r cos ∅

y = r sin ∅

z = \sqrt{3x^2 + 3y^2} = \sqrt{3r}

next we calculate the surface charge density of the cone

б ( r, ∅ ) = xyz^2 = 3r^4 sin∅ cos∅

Charge given as

Q = ∫ б(r,∅ )ds

   = ∫ б(r,∅ ) \sqrt{1 +( \frac{dz}{dx})^2 + (\frac{dz}{dx} )^2 }   dA

after integration

Q  = ∫ б(r,∅ ) 2dA

Attached below is the remaining part of the solution

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