Electromagnetic Waves — Physics STD 12 Science — Question

Consider a situation similar to that of the previous problem except that the ends of the rod slide on a pair of thick metallic rails laid parallel to the wire. At one end the rails are connected by resistor of resistance R.

1. What force is needed to keep the rod sliding at a constant speed v?
2. In this situation what is the current in the resistance R?
3. Find the rate of heat developed in the resistor.
4. Find the power delivered by external agent exerting the force on the rod.

Two circular coils of radii 5.0cm and 10cm carry equal currents of 21 A. The coils have 50 and 100 turns reepectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.

Two circular coils of radii 5.0cm and 10cm carry equal currents of 21 A. The coils have 50 and 100 turns reepectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.

Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10^–10m).

1. Construct a quantity with the dimensions of length from the fundamental constants e, m_e, and c. Determine its numerical value.
2. You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, me, and e will yield the right atomic size. Construct a quantity with the dimension of length from h, m_e, and e and confirm that its numerical value has indeed the correct order of magnitude.

When an electron goes from the valence band to the conduction band in silicon, its energy is increased by 1.1eV. The average energy exchanged in a thermal collision is of the order of kT which is only 0.026eV at room temperature. How is a thermal collision able to take some of the electrons from the valence band to the conduction band?

Figure shows a small body of mass m placed over a larger mass M whose surface is horizontal near the smaller mass and gradually curves to become vertical. The smaller mass is pushed on the longer one at a speed v and the system is left to itself. Assume that all the surfaces are frictionless.

1. Find the speed of the larger block when the smaller block is sliding on the vertical part.
2. Find the speed of the smaller mass when it breaks off the larger mass at height h.
3. Find the maximum height (from the ground) that the smaller mass ascends.
4. Show that the smaller mass will again land on the bigger one. Find the distance traversed by the bigger block during the time when the smaller block was in its flight under gravity.

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A ball is thrown horizontally from a point 100m above the ground with a speed of 20m/s. Find:

1. The time it takes to reach the ground.
2. The horizontal distance it travels before reaching the ground.
3. The velocity (direction and magnitude) with which it strikes the ground.