Explanation Given: The solid region is the ball defined by x 2 + y 2 + z 2 ≤ 5 (in centimetres), and the charge density is δ ( x , y , z ) = ( 3 ⋅ 10 − 8 ) ( x 2 + y 2 + z 2 ) 1 2 coulombs per cubic centimetres. Formula used: The total charge of a region W with a given charge density of δ ( x , y , z ) is the solution of the integration ∭ V δ ( x , y , z ) d V (in 3-dimention) where d V is an elementary volume of the region W . Calculation: Here the region is the given solid ball, So, ∭ V δ ( x , y , z ) d V = ∭ V ( 3 ⋅ 10 − 8 ) ( x 2 + y 2 + z 2 ) 1 2 d z d y d x Now if we turn it into spherical co-ordinates, that is x = ρ sin θ cos ϕ y = ρ sin θ sin ϕ z = ρ cos θ Then d z d y d x = ρ 2 sin θ d ρ d θ d ϕ 0 ≤ ρ ≤ 5 ; 0 ≤ θ ≤ π 0 ≤ ρ ≤ 5 ; 0 ≤ θ ≤ π With 0 ≤ ρ ≤ 5 ; 0 ≤ θ ≤ π ; 0 ≤ ϕ ≤ 2 π So, the i...

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Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.5, Problem 7E

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The total charge of a solid ball assuming a charge density of $δ (x, y, z)$

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Chapter 16.5, Problem 6E

Chapter 16.5, Problem 8E

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The total charge of a solid ball assuming a charge density of δ ( x , y , z )

Solution Summary: The author explains how to determine the total charge of a solid ball based on x, y, and z.

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The total charge of a solid ball assuming a charge density of δ ( x , y , z )

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The total charge of a solid ball assuming a charge density of δ(x,y,z)

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The total charge of a solid ball assuming a charge density of $δ (x, y, z)$