1
AIEEE 2010
+4
-1
Let there be a spherically symmetric charge distribution with charge density varying as $$\rho \left( r \right) = {\rho _0}\left( {{5 \over 4} - {r \over R}} \right)$$ upto $$r=R,$$ and $$\rho \left( r \right) = 0$$ for $$r>R,$$ where $$r$$ is the distance from the erigin. The electric field at a distance $$r\left( {r < R} \right)$$ from the origin is given by
A
$${{{\rho _0}r} \over {4{\varepsilon _0}}}\left( {{5 \over 3} - {r \over R}} \right)$$
B
$${{4\pi {\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 3} - {r \over R}} \right)$$
C
$${{4{\rho _0}r} \over {4{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)$$
D
$${{{\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)$$
2
AIEEE 2010
+4
-1
A thin semi-circular ring of radius $$r$$ has a positive charges $$q$$ distributed uniformly over it. The net field $$\overrightarrow E$$ at the center $$O$$ is
A
$${q \over {4{\pi ^2}{\varepsilon _0}{r^2}}}\,j$$
B
$$- {q \over {4{\pi ^2}{\varepsilon _0}{r^2}}}\,j$$
C
$$- {q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j$$
D
$${q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j$$
3
AIEEE 2009
+4
-1
Let $$P\left( r \right) = {Q \over {\pi {R^4}}}r$$ be the change density distribution for a solid sphere of radius $$R$$ and total charge $$Q$$. For a point $$'p'$$ inside the sphere at distance $${r_1}$$ from the center of the sphere, the magnitude of electric field is :
A
$${Q \over {4\pi \,{ \in _0}\,r_1^2}}$$
B
$${{Qr_1^2} \over {4\pi \,{ \in _0}\,{R^4}}}$$
C
$${{Qr_1^2} \over {3\pi \,{ \in _0}\,{R^4}}}$$
D
$$0$$
4
AIEEE 2009
+4
-1
(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.)

Statement-1 : For a charged particle moving from point $$P$$ to point $$Q$$, the net work done by an electrostatic field on the particle is independent of the path connecting point $$P$$ to point $$Q.$$
Statement-2 : The net work done by a conservative force on an object moving along a closed loop is zero.

A
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
B
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
C
Statement- 1 is false, Statement- 2 is true.
D
Statement- 1 true, Statement- 2 is false
EXAM MAP
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