1
AIEEE 2010
+4
-1
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $${30^ \circ }$$ with each other. When suspended in a liquid of density $$0.8g$$ $$c{m^{ - 3}},$$ the angle remains the same. If density of the material of the sphere is $$1.6$$ $$g$$ $$c{m^{ - 3}},$$ the dielectric constant of the liquid is
A
$$4$$
B
$$3$$
C
$$2$$
D
$$1$$
2
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
$${{{\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)$$
3
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
$${q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j$$
4
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
$$0$$
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