Unit Test — I (2022-2023)
Class XII
Physics
Time: 1 Hour
M.M. — 20
Section — A
1. Draw equipotential surfaces for an electric dipole. (1)
2. Which charge configuration produces a uniform electric field? (1)
a) point charge
b) infinite uniform line charge
c) uniformly charged infinite plane
d) uniformly charged spherical shell
3. An electric dipole is placed at an alignment angle of 30° with an electric field of 2×10^5 N/C. It experiences a torque equal to 8 Nm. The charge on the dipole if the dipole length is 1 cm is
a) 4 mC
b) 8 mC
c) 5 mC
d) 7 mC
4. Rank the electrostatics potential energies for the given system of charges in increasing order. (1)
a) 1=4<2<3
b) 2=4<3<1
c) 2=3<1<4
d) 3<1<2<4
5. Write the dimensions of electric flux and capacitance of the capacitor. (1)
Section — B
6. A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q. (2)
(a) A charge q is placed at the centre of the shell. Find out the surface charge density on the inner and outer surfaces of the shell.
(b) Is the electric field inside a cavity (with no charge) zero; independent of the fact whether the shell is spherical or not? Explain
7. In the network, four capacitors C1, C2, C3 and C4 are connected as shown in the figure. (2)
a) If the charge on the capacitor C1 is 6µC,
(i) Calculate the charge on the capacitors C3 and C4, and
(ii) net energy stored in the capacitors C3 and C4 connected in series.
Section — C
8. Two large charged plane sheets of charge densities σ and -2σ C/m2 are arranged vertically with a separation of d between them. Deduce expressions for the electric field at points (i) to the left of the first sheet, (ii) to the right of the second sheet, and (iii) between the two sheets. (3)
OR
Calculate the potential difference and the energy stored in the capacitor C2 in the circuit shown in the figure. Given potential at A is 90 V, C1=20µF, C2=30µF and C3=15µF. (3)
9. Derive electrical potential energy due to a dipole placed in a uniform electric field. (3)
Section — D (5 Marks)
10. (a) Define electric flux. “Gauss law in electrostatics is true for any closed surface, no matter what its shape or size is”. Justify this statement with the help of a suitable example.
b) Use Gauss’s law to prove that electric field inside a uniformly charged spherical shell is zero.
c) A fully charged parallel plate capacitor is connected across an uncharged identical capacitor. Show that the energy stored in the combination is less than that stored initially in the single capacitor.