11.
A point charge $$+Q$$ is positioned at the center of the base of a square pyramid as shown. The flux through one of the four identical upper faces of the pyramid is
A
$$\frac{Q}{{16{\varepsilon _0}}}$$
B
$$\frac{Q}{{4{\varepsilon _0}}}$$
C
$$\frac{Q}{{8{\varepsilon _0}}}$$
D
0
Answer :
$$\frac{Q}{{8{\varepsilon _0}}}$$
12. An electric dipole is put in north-south direction in a sphere filled with water. Which statement is correct?
A
Electric flux is coming towards sphere.
B
Electric flux is coming out of sphere.
C
Electric flux entering into sphere and leaving the sphere are same.
D
Water does not permit electric flux to enter into sphere.
Answer :
Electric flux entering into sphere and leaving the sphere are same.
13. A hollow metal sphere of radius $$5 cms$$ is charged such that the potential on its surface is $$10\,volts.$$ The potential at the centre of the sphere is
A
zero
B
$$10\,volts$$
C
same as at a point $$5 cms$$ away from the surface
D
same as at a point $$25 cms$$ away from the surface
Answer :
$$10\,volts$$
14.
A uniformly charged and infinitely long line having a linear charge density $$\lambda $$ is placed at a normal distance $$y$$ from a point $$O.$$ Consider an imaginary sphere of radius $$R$$ with $$O$$ as centre and $$R > y.$$ Electric flux through the surface of the sphere is
A
zero
B
$$\frac{{2\lambda R}}{{{\varepsilon _0}}}$$
C
$$\frac{{2\lambda \sqrt {{R^2} - {y^2}} }}{{{\varepsilon _0}}}$$
D
$$\frac{{\lambda \sqrt {{R^2} + {y^2}} }}{{{\varepsilon _0}}}$$
Answer :
$$\frac{{2\lambda \sqrt {{R^2} - {y^2}} }}{{{\varepsilon _0}}}$$
15.
$$A,B$$ and $$C$$ are three points in a uniform electric field. The electric potential is
A
maximum at $$A$$
B
maximum at $$B$$
C
maximum at $$C$$
D
same at all the three points $$A,B$$ and $$C$$
Answer :
maximum at $$B$$
16. A charge $$q$$ is located at the centre of a cube. The electric flux through any face is
A
$$\frac{{\pi q}}{{6\left( {4\pi {\varepsilon _0}} \right)}}$$
B
$$\frac{q}{{6\left( {4\pi {\varepsilon _0}} \right)}}$$
C
$$\frac{{2\pi q}}{{6\left( {4\pi {\varepsilon _0}} \right)}}$$
D
$$\frac{{4\pi q}}{{6\left( {4\pi {\varepsilon _0}} \right)}}$$
Answer :
$$\frac{{4\pi q}}{{6\left( {4\pi {\varepsilon _0}} \right)}}$$
17. A charge is situated at a certain distance from an electric dipole in the end-on position experiences a force $$F.$$ If the distance of the charge is doubled, the force acting on the charge will be
A
$$\frac{F}{4}$$
B
$$\frac{F}{8}$$
C
$$2F$$
D
$$\frac{F}{2}$$
Answer :
$$\frac{F}{8}$$
18. The insulation property of air breaks down when the electric field is $$3 \times {10^6}V{m^{ - 1}}.$$ The maximum charge that can be given to a sphere of diameter $$5\,m$$ is approximately
A
$$2 \times {10^{ - 2}}\,C$$
B
$$2 \times {10^{ - 3}}\,C$$
C
$$2 \times {10^{ - 4}}\,C$$
D
$$2 \times {10^{ - 5}}\,C$$
Answer :
$$2 \times {10^{ - 3}}\,C$$
19.
The electric potential at a point $$\left( {x,y,z} \right)$$ is given by $$V = - {x^2}y - x{z^3} + 4$$
The electric field $$E$$ at that point is
A
$$E = \left( {2xy + {z^3}} \right)\hat i + {x^2}\hat j + 3x{z^2}\hat k$$
B
$$E = 2xy\hat i + \left( {{x^2} + {y^2}} \right)\hat j + \left( {3xz - {y^2}} \right)\hat k$$
C
$$E = {z^3}\hat i + xyz\hat j + {z^2}\hat k$$
D
$$E = \left( {2xy - {z^3}} \right)\hat i + x{y^2}\hat j + 3{z^2}x\hat k$$
Answer :
$$E = \left( {2xy + {z^3}} \right)\hat i + {x^2}\hat j + 3x{z^2}\hat k$$
20.
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
Answer :
non-zero and uniform
