1
AIEEE 2012
+4
-1
This question has statement- $$1$$ and statement- $$2.$$ Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius $$R$$ has a uniformly positive charge density $$\rho$$. As a result of this uniform charge distribution there is a finite value of electric potential at the center of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.

Statement- $$1:$$ When a charge $$q$$ is take from the centre of the surface of the sphere its potential energy changes by $${{q\rho } \over {3{\varepsilon _0}}}$$
Statement- $$2:$$ The electric field at a distance $$r\left( {r < R} \right)$$ from the center of the sphere is $${{\rho r} \over {3{\varepsilon _0}}}.$$

A
Statement- $$1$$ is true, Statement- $$2$$ is true; Statement- $$2$$ is not the correct explanation of Statement- $$1$$.
B
Statement $$1$$ is true, Statement $$2$$ is false.
C
Statement $$1$$ is false, Statement $$2$$ is true.
D
Statement- $$1$$ is true, Statement- $$2$$ is true; Statement- $$2$$ is the correct explanation of Statement- $$1$$.
2
AIEEE 2012
+4
-1
In a uniformly charged sphere of total charge $$Q$$ and radius $$R,$$ the electric field $$E$$ is plotted as function of distance from the center. The graph which would correspond to the above will be:
A
B
C
D
3
AIEEE 2011
+4
-1
The electrostatic potential inside a charged spherical ball is given by $$\phi = a{r^2} + b$$ where $$r$$ is the distance from the center and $$a,b$$ are constants. Then the charge density inside the ball is:
A
$$- 6a{\varepsilon _0}r$$
B
$$- 24\pi a{\varepsilon _0}$$
C
$$- 6a{\varepsilon _0}$$
D
$$- 24\pi {\varepsilon _0}r$$
4
AIEEE 2011
+4
-1
Two identical charged spheres suspended from a common point by two massless strings of length $$l$$ are initially a distance $$d\left( {d < < 1} \right)$$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $$v$$. Then as a function of distance $$x$$ between them,
A
$$v\, \propto \,{x^{ - 1}}$$
B
$$y\, \propto \,{x^{{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}}$$
C
$$v\, \propto \,x$$
D
$$v\, \propto \,{x^{ - {\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}}$$
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