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Question
A spherical volume contains a uniformly distributed charge of density 2.0 × 10 -4 Cm-3 Find the electric field at a point inside the volume at a distance 4⋅0 cm from the centre.
Solution
Given :
Volume charge density, ρ = 2 ×10-4 C /m3
Let us assume a concentric spherical surface inside the given sphere with radius = 4 cm = 4 ×10-2 m
The charge enclosed in the spherical surface assumed can be found by multiplying the volume charge density with the volume of the sphere. Thus,
`"q" = ρ xx 4/3 pi"r"^3`
`=> "q"= (2 xx 10^-4) xx 4/3 pi"r"^3`
The net flux through the spherical surface,
`phi ="q"/∈_0`
The surface area of the spherical surface of radius r cm:
A = 4πr2
Electric field,
`"E" = "q"/(∈_0 xx "A")`
`"E" = (2 xx 10^-4 xx 4 pi "r"^3)/(∈_0 xx 3 xx 4 pi"r"^2)`
`"E" = (2 xx 10 ^-4 xx "r")/(3 xx ∈ _0)`
The electric field at the point inside the volume at a distance 4⋅0 cm from the centre,
`"E" = ((2 xx 10^-4) xx (4 xx 10^-2))/(3 xx (8.55 xx 10^-12)) "N" // "C"`
`"E" = 3.0 xx 10^5 "N" // "C"`
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