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'slaw i.e.,
Total electric flux on the sphere of radius `r= 0.2 m` is equal to ` ( 1)/ ( epsilon_(0))` times the charge enclosedbythe 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 4 pi r^(2) = (Q)/( epsilon_(0))`
or , `( 250 r ) ( 4pi r^(2))= ( Q)/( epsilon_(0)) impliesQ = 1000 pi r^(3)epsilon_(0)= 2.22 xx 10^(-10)C`
`( r = 0.2 m ` and `(1)/( 4pi epsilon_(0))= 9 xx 10^(9) ( Nm^(2))/(C^(2)))`

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The electric field in a region is radially outward and at a point is given by E=250" r V"//"m" (where r is the distance of the point from origin). Calculate the charge contained in a sphere of radius 20 cm centred at the origin

`2.22xx10^(-6)C`

`2.22xx10^(-10)C`

Zero

The electric field in a region is radially outward with magnitude E = (A)/(gamma) . The charge contained in a sphere of radius gamma_(0) centered at the origin is

`(1)/(4piepsi_(0)) Agamma_(0)^(2)`

`4piepsi_(0)Agamma_(0)`

`(4piepsi_(0)A)/(gamma_(0))`

`(1)/(4piepsi_(0)) (A)/(gamma_(0))`

In a region where E = 0, the potential (V) varies with distance r as -

`V alpha (1)/(r )`

`V alpha r`

`V alpha (1)/(r^(2))`

V = const. independent of (r )