IIT - JEE Advanced

Point 1: For case for ground pin. Also ground pin is larger that other two pins so that it would be the first to go into the hole and the last to come out of the hole just for sake of safety

Point 2: This is done to prevent the user from accidentally inserting the live or neutral pin into the ground pin.

Point 3: It is because of simple thing:

i. If all are same sized then you will have 3 choices to plug in but every time you will not make it right so you get confusion.

ii. In order to eliminate that one of them is bigger than remaining ones so that every time you plugin you will get supply even if you use 2 pin plug.

Point 4: R proportional to L/A. So larger the cross sectional area lesser the resistance!  So with less resistance in case of fault all the current will pass through that pin(which is the ground) and make no harm to your circuit! Basically its for electrical safety!

The curves that we learn about in this chapter are called conic sections. They arise naturally in many situations and are the result of slicing a cone at various angles.

Depending on where we slice our cone, and at what angle, we will either have a straight line, a circle, a parabola, an ellipse or a hyperbola. Of course, we could also get a single point, too.

Why study analytic geometry?

Science and engineering involves the study of quantities that change relative to each other (for example, distance-time, velocity-time, population-time, force-distance, etc).

It is much easier to understand what is going on in these problems if we draw graphs showing the relationship between the quantities involved.

The study of calculus depends heavily on a clear understanding of functions, graphs, slopes of curves and shapes of curves. For example, in the Differentiation chapter we use graphs to demonstrate relationships between varying quantities.

Solving a mechanics problem especially at JEE level is all about getting into right thinking framework. 

Step 1: Picking a frame of reference. It can be solved from inertial frame of reference or non-nertial frame of reference (where a pseudo force acts).

Step 2: Divide the problem into small parts and then draw the free body diagrams.

Step 3: Use the Newton's 3 Laws to write the equations.

Step 4: Solve the equations to get the answer.

Is self induced emf in an inductor will be equal and opposite to the applied voltage? If yes then why current flow in the circuit?

1. i. State Ampere's circuit law.

ii. A hollow conducting cylinder has inner radius a and outer radius b and carries current I along the positive z-direction. Find H everywhere.

2. Find H at the center C of an equilateral triangular loop of side 4 m carrying 5 A of current.

3. A thin plastic disk of radius R has a uniform charge density. The disk is rotating about its axis with an angular speed. Find the magnetic field along the axis of the disk at a distance z from the centre.

4. Two parallel current carrying wires of length L and mass m per unit length each are suspended from the ceiling by means of massless strings of length l each. The wires carry equal currents in opposite directions. If the angle between the wires suspended from the same point is θ, obtain an expression for the current flowing in each wire in terms of the given quantities.

5. i. A filamentary loop carrying current I is bent to assume the shape of a regular polygon of n sides. Circumscribing a circle of radius r. Find H at the centre of the polygon.

ii. Show that if n approaches infinity, the result obtained is the same as that of a circle.

6. A massless conducting rod of resistance R lies on two perfectly conducting horizontal rails separated by a distance d on a table, at one end the rods are connected by a conducting wire. A vertically upward magnetic field B exists in the region. If the rod is connected by a pulley arrangement which supports a mass m which falls down as the rod moves outward on the rails. Calculate the terminal velocity of the mass.

7. Arrive at Maxwell's corrections to Ampere's Law. Explain its significance and hence arrive at the wave equation for EM Waves.

1. One of the following is not a source of magnetostatic fields: 

a. A dc current in a wire.

b. A permanent magnet.

c. An accelerated charge.

d. An electric field Linearly changing with time.

e. A charged disk rotating at uniform speed.

2. Which of these statements is not characteristic of a static magnetic field?

a. It is solenoidal.

b. It is conservative.

c. It has no sinks or sources.

d. Magnetic flux lines are always closed.

e. The total number of flux lines entering a given region is equal to the total number of flux lines leaving the region.

3. Two identical circular coaxial coils carry current I in opposite directions. The magnetic field H at a point on the axis, midway between the coils is:

a. Zero.

b. The same as that produced by one coil.

c. Twice that produced by one coil.

d. Half that produced by one coil.