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The electric field in a region is radial...

The electric field in a region is radially outward and varies with distance r as `E = 250` r ( volt per square metre).Calculate the charge contained in a sphere of radius 0.2 m centeredat the origin.

Text Solution

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Use Gauss.s law i.e.,
Total electric flux on the sphere of radius r = 0.2 m is equal to `(1)/(epsilon_(0))` times the charge enclosed by the sphere. Since E is dependent just on r, so it is a case of spherical symmetry and hence, Gaussian surface taken has been a sphere.
So, `E.4pi r^(2)=(Q)/(epsilon_(0))`
or, `(250r)(4pi r^(2))=(Q)/(epsilon_(0))impliesQ=1000pi r^(3)epsilon_(0)=2.22xx10^(-10)C`
`(r=0.2"m and"(1)/(4pi epsilon_(0))=9xx10^(9)(Nm^(2))/(C^(2)))`
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