Linear Induction Motor

Problem:

The concept of a linear induction motor is used to develop a magnetically levitated high speed train. The engine car carries a 3 phase 10 pole winding placed in a linear configuration. The dimensions of the winding configuration of the car is of 10 m length ( in the direction of movement of the train) and 4 m wide excluding end winding. This winding is facing the track which is a linear dispossessed squirrel cage winding. The air gap is sandwiched between the above two. Determine the supply frequency to run the train near 400 Km/ hr. [IIT DELHI]

Square Loop in a Magnetic Field

Problem:

A rectangular frame ABCD made of auniform metal wire has a straight connection between E & F made of the same wire as shown in the figure. AEFD is a square of side 1 m & EB = FC = 0.5 m. The entire circuit is placed in a steadily increasing uniform magnetic field directed into the place ofthe paper & normal to it. The rate of change of the magnetic field is 1 T/s, the resistance per unit length ofthe wire is 1 $\Omega$/m. Find the current in segments AE, BE & EF. [IIT JEE'93]

Electron entering a capacitor

Problem:

An electron enters the region between the plates of a parallel plate capacitor at a point equidistant from either plate. The capacitor plates are $2* 10^{-2}$ m apart & $10^{-1}$ m long. A potential difference of 300 volt is kept across the plates. Assuming that the initial velocity of the electron is parallel to the capacitor plates, calculate the largest value of the velocity of the electron so that they do not fly out of the capacitor at the other end. [IIT JEE]

Capacitor Circuit

Problem:

Two capacitors A and B with capacities 3 pF and 2 pF are charged to a potential difference of 100 V and 180 V respectively. The plates of the capacitors are connected as shown in figure with one wire from each capacitor free. The upper plate of a is positive and that of B is negative, an uncharged 2 pF capacitor C with lead wires falls on the free ends to complete the circuit. Calculate the final charges on the three capacitors and the amount of electrostatic energy stored in the system before and after the completion of the circuit. [IIT JEE'97]

Capacitance

Problem:

The capacitance of a parallel plate capacitor with plate area $A$ & separation $d$ is $C$. The space between the plates is filled with two wedges of di-electric constant $K_{1}$ & $K_{2}$ respectively. Find the capacitance of the resulting capacitor. [IIT JEE'96]

Electricity & Magnetism S S Krotov

Problem:

A concealed circuit consisting of resistors has four terminals as shown in fig. If a voltage is applied between clamps 1 and 2 when 3 and 4 are disconnected power liberated is $P_{1}=$ 40 W. When clamps 3 and 4 are connected $P_{2}=$ 80 W. If the same source is connected to the clamps 3 and 4, the power liberated when 1 and 2 are disconnected $P_{3}=$ 20 W. Determine the power $P_{4}$ with 1 and 2 shorted with the same source applied between 3 and 4.

Mechanics question from Book by S S Krotov

Problem:

Small balls with zero initial velocity fall from a height $H = \displaystyle\frac{R}{8}$ near the vertical axis of symmetry on a concave spherical surface of radius $R$. Assuming that the impacts of the balls against the surface are perfectly elastic, prove that after the first impact each ball gets into the lowest point of the spherical surface.

Conductor Harmonic Motion - IIT JEE 2003

Problem:

Along horizontal wire AB, which is free to move in a vertical plane and carries a steady current of 20 A, is in equilibrium at a height of 0.01 m over another parallel long wire CD which is fixed in a horizontal plane and carries a steady current of 30 A. Show that when AB is slightly depressed, it executes simple harmonic motion. Find the period of oscillations.

Find value of Resistance - IIT JEE 2005

Problem:

In the figure both cells A and B are of equal emf. Find R for which potential difference across battery A will be zero, long time after the switch is closed. Internal resistance of batteries A and B are $r_{1}$ and $r_{2 }$respectively ($r_{1}>r_{2 }$).

Kinetic Theory of Gases - IIT JEE 1993

The following problem appeared in the Physics paper of IIT JEE 1993. It still considered to be one of the most formidable problems ever asked in the history of the exam.

Problem:

A neutron of kinetic energy 65 eV collides in-elastically with a singly ionized helium atom at rest. It is scattered at an angle of 90º with respect of its original direction.

(i) Find the allowed values of the energy of the neutron and that of the atom after the collision.

(ii) If the atom get de-excited subsequently by emitting radiation, find the frequencies of the emitted radiation. [Given: mass of He atom =4×(mass of neutron),Ionization energy of He atom = 13.6 eV]