1
IIT-JEE 2008 Paper 2 Offline
+3
-1

The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $$\rho(r)$$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as 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
2
IIT-JEE 2008 Paper 2 Offline
+3
-1

The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $$\rho(r)$$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as 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

A
$${{3Ze} \over {4\pi {R^3}}}$$
B
$${{3Ze} \over {\pi {R^3}}}$$
C
$${{4Ze} \over {3\pi {R^3}}}$$
D
$${{Ze} \over {3\pi {R^3}}}$$
3
IIT-JEE 2008 Paper 2 Offline
+3
-1

The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $$\rho(r)$$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction. The electric field within the nucleus is generally observed to be linearly dependent on r. This implies

A
$$a = 0$$
B
$$a = {R \over 2}$$
C
$$a = R$$
D
$$a = {{2R} \over 3}$$
4
IIT-JEE 2007 Paper 2 Offline
+3
-1

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is A
zero everywhere
B
non-zero and uniform
C
non-uniform
D
zero only at its center
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