AGARWAL’S PHYSICS RAVI AGARWAL (M.Sc.) – 9913650950 / 9374727052TIME: 1Hr.30 min. CH.1 to 5(Numericals) Marks: 50

1 A charge Q is uniformly spread over a disc of radius R, made from a non-conducting material. This disc is now rotated about its geometrical axis with frequency f. Find the magnetic field generated at the center of the disc.

2 Q amount of electric charge is uniformly distributed on a ring of radius r. A sphere of radius r is drawn in such a way that the center of the sphere lies on the surface of the ring. Calculate the electric flux associated with the surface of the sphere.

3 A thin layer of 0.001 cm of copper is to be deposited on a plate of copper of 10cm2

through electrolysis. Calculate the amount of energy used if a battery of 12V is connected. Density of copper = 9g/cm3, electrochemical equivalent of copper = 0.0003g/mol.

4 A capacitor of 4pF value is charged to 50V. The above capacitor is then connected in paralled to a 2 pF capacitor. Calculate the total energy of the above system. The second capacitor is not charged prior to its connection with the 4 pF capacitor. Ignore the energy loss in the above process.

5 Copper wire of 0.2 mm diameter is connected to iron wire of 5.0 mm diameter. The current flows through both the wires. If 8.0 A current flows through the copper wire, then calculate the following quantities.

(i) The current following through the iron wire and its current density.(ii) The current density in the copper wire.

6 The atomic weight of copper is 63.54 g/mol. Its density = 8.9 × 103 Kgm-3. If its valency is 1, find the free electron number density. Avogadro number = 6.02 × 1023 mol-1

7 Obtain the expression for the magnetic field at the midpoint on the axis of a solenoid with n turns per unit length of length L, radius a and current carrying is I unit.

8 An electric dipole of moment is placed in a uniform electric field. The dipole is rotated through a very small angle θ from equilibrium and is released. Prove that it executes angular simple harmonic motion and find frequency.

9 A very long wire is placed perpendicular to the direction of horizontal component of earth’s magnetic field. Find the value of current to be passed through the wire so that the resultant magnetic field is zero at a point which is at a distance of 5cm from the wire. What will be the magnetic field at a point at a distance of 5cm from the wire on the opposite side? H=0.36×10-4T.

10 A copper wire is stretched to increase its length by 1%. Calculate the % change in the resistance.

11 α1 and α2 of two materials are 6×10-4℃-1 and -5×10-4 ℃-1. For the first material, the resistivity ρ20 = 2×10-8 Ωm. A new material has to be prepared by the mixture of these two materials such that it resistivity does not change with temperature. What should be the value of ρ20 of the second material? Take reference temperature = 20℃. Assume that resistivity of the mixture is equal to the sum of resistivity of the two materials.

12 Copper wire is used in the wiring of the house. This wire is normally of 12 gauge. The resistivity of the copper at 20℃ temperature is 1.77 × 10-8Ωm. Calculate the resistance of 10m long wire at this temperature. 12 gauge=2.05×10-3m diameter.

13 A spherical drop of water has charge of 3 × 10-10 C. The electric potential on its surface is 500V. Calculate the radius of the drop. Two such identical drops with equal charges combine to form a drop. Calculate the electric potential on the surface of the new drop. (k = 9 × 109 SI)

14 Prove that the force acting on one plate due to the other in a parallel plate capacitor is given by F=CV2/2d.

15 A circular loop is prepared from a wire of uniform cross section. A battery is connected between any two points on its circumference. Show that the magnetic induction at the center of the loop is zero.

16 Two wires of the same material having same cross sectional area, having length l1and l2. They are to be used as fuse wires. Prove that when currents through them will be equal, they will start melting in the same time interval.

17 The resistance of an ammeter is 0.01Ω. The ammeter shows 4A current where it is connected with the battery. The current is reduced to three A when a 1.5 Ω resistor is connected in series. Calculate the emf of the battery and its internal resistance.

18 Two rings X and Y are placed in such a way that their axes are along X and the Y axes respectively and centers of both the rings are at the origin. Both the rings have the same radii of 3.14cm. If the current through the ringX is 0.4A and through the ringY is 0.3A, find the intensity of the resultant magnetic field at the origin.

WINNERS DON’T DO DIFFERENT THINGS THEY DO THE THINGS DIFFERENTLY. Shiv khera