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The nuclear charge (Ze) is non uniformll...

The nuclear charge (`Ze`) is non uniformlly distribute with in a nucleus of radius r. The charge density `rho(r)` (charge per unit volume) is dependent only on the radial distance r form the centre of the nucleus s shown in figure. The electric field is only along the radial direction.

The electric field at `r=R` is

A

Independent of a

B

Directly proportional to a

C

Directly proportional to `a^(2)`

D

Inversely proportional to a

Text Solution

Verified by Experts

The correct Answer is:
A
`E(4pi R^(2))=((Ze))/in_(0)rArr E=(Ze)/(4pi in_(0) R^(2))`
`rArr` Independent of a
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The nuclear charge ( Ze ) is non uniformlly distribute with in a nucleus of radius r. The charge densilty rho(r) (charge per unit volume) is dependent only on the radial distance r form the centre of the nucleus s shown in figure. The electric field is only along the radial direction. The electric field within the nucleus is generaly observed to be linearly dependent on r. This implies

The nuclear charge ( Ze ) is non uniformlly distribute with in a nucleus of radius r . The charge density rho(r) (charge per unit volume) is dependent only on the radial distance r form the centre of the nucleus s shown in figure. The electric field is only along the radial direction. For a=0 the value of d (maximum value of rho as shown in the figure) is

Knowledge Check

  • A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre

    A
    increases as r increases for r lt R and for r gt R
    B
    zero as r increases for r lt R, decreases as r increases for r gt R.
    C
    zero as r increases for r lt R, increases as r increases for r gt R.
    D
    decreases as r increases for r lt R and for r gt R.

  • A positive charge Q is uniformly distribut along a circular ring of radius R. A small tc charge q is placed at the centre of the ring per figure, Then

    A
    If q gt 0 and is displaced away from th centre in the plane of the ring, it will b pushed back towards the centre.
    B
    If q lt 0 and is displaced away from the centr in the plane of the ring, it will never return ti the centre and will continue moving till I hits the ring.
    C
    If q lt 0, it will perform SHM for smai displacement along the axis.
    D
    q at the centre of the ring is in an unstabh equilibrium within the plane of the ring fo q gt 0

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