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A charge +Q, is uniformaly distributed w...

A charge `+Q`, is uniformaly distributed within a sphere of radius R. Find the electric field, due to this charge distribution, at a point distant r form the centre of the spehre where :
(i) ` 0 lt r lt R` and
`(ii) r gt R`

Text Solution

AI Generated Solution

To find the electric field due to a uniformly distributed charge \( +Q \) within a sphere of radius \( R \) at a point distant \( r \) from the center of the sphere, we will consider two cases: ### Case (i): \( 0 < r < R \) 1. **Determine the volume charge density**: The volume charge density \( \rho \) is given by: \[ \rho = \frac{Q}{\frac{4}{3} \pi R^3} ...
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Knowledge Check

  • Charges q is uniformly distributed over a thin half ring of radius R . The electric field at the centre of the ring is

    A
    `(q)/(2pi^(2)epsilon_(0)R^(2))`
    B
    `(q)/(4pi^(2)epsilon_(0)R^(2))`
    C
    `(q)/(4piepsilon_(0)R^(2))`
    D
    `(q)/(2piepsilon_(0)R^(2))`
  • A hollow metal sphere of radius R is uniformly charged The electric field due to the spehre at a distance r from the centre

    A
    Increases as r increases for `rltRand` for `rgtR`
    B
    Zero as r increases for `rltR`, decreases as r increases for `rgtR`
    C
    Zero as r increases for `rltR` , increases as r increases for `rgtR`
    D
    Decreases as r increases for `rltRand` for `rgtR`
  • A hallow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre:

    A
    decreases as r increases for `rltR` and `rgtR`
    B
    increases as r increases for `rltR` and `rgtR`
    C
    zero as r increases for `rltR`, decreases as r increases for `rgtR`
    D
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