1
IIT-JEE 2010 Paper 2 Offline
+2
-0.5
A tiny spherical oil drop carrying a net charge $$q$$ is balanced in still air with a vertical uniform electric field of strength $${{81\pi } \over 7} \times {10^5}\,\,V{m^{ - 1}}.$$ When the field is switched off, the drop is observed to fall with terminal velocity $$2 \times {10^{ - 3}}\,\,m{s^{ - 1}}.$$ Given $$g = 9.8\,m\,{s^{ - 2}},$$ viscosity of the air $$= 1.8 \times {10^{ - 5}}\,\,Ns\,{m^{ - 2}}$$ and the density of coil $$=900$$ $$kg$$ $${m^{ - 3}},$$ the magnitude of $$q$$ is
A
$$1.6 \times {10^{ - 19}}C$$
B
$$3.2 \times {10^{ - 19}}C$$
C
$$4.8 \times {10^{ - 19}}C$$
D
$$8.0 \times {10^{ - 19}}C$$
2
IIT-JEE 2010 Paper 2 Offline
+2
-0.5
A uniformly charged thin spherical shell of radius $$R$$ carries uniform surface charge density of $$\sigma$$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $$F$$ (see figure). $$F$$ is proportional to

A
$${1 \over {{\varepsilon _0}}}{\sigma ^2}{R^2}$$
B
$${1 \over {{\varepsilon _0}}}{\sigma ^2}R$$
C
$${1 \over {{\varepsilon _0}}}{{{\sigma ^2}} \over R}$$
D
$${1 \over {{\varepsilon _0}}}{{{\sigma ^2}} \over {{R^2}}}$$
3
IIT-JEE 2009 Paper 1 Offline
+3
-1

A disk of radius $${a \over 4}$$ having a uniformly distributed charge 6C is placed in the xy-plane with its centre at ($$-$$a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two points charges $$-$$7C and 3C are placed at (a/4, $$-$$a/4, 0) and ($$-$$3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces $$x=\pm a/2,y=\pm a/2,z=\pm a/2$$. The electric flux through this cubical surface is

A
$${{ - 2c} \over {{\varepsilon _0}}}$$
B
$${{2c} \over {{\varepsilon _0}}}$$
C
$${{10c} \over {{\varepsilon _0}}}$$
D
$${{12c} \over {{\varepsilon _0}}}$$
4
IIT-JEE 2009 Paper 1 Offline
+3
-1

Three concentric metallic spherical shells of radii $$R,2R,3R$$ are given charges $$Q_1,Q_2,Q_3$$, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, $$Q_1:Q_2:Q_3$$, is

A
1 : 2 : 3
B
1 : 3 : 5
C
1 : 4 : 9
D
1 : 8 : 18
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