Solenoid

A long solenoid with its axis as the z-axis and uniform cross-section perpendicular to the z-axis carries a current I and has a turn density n in vacuum.

Compute the magnetic field it produces everywhere if its cross-section is circular.

Click here when you've done this.

Click here for the solution.

Hourglass

A "water"-hourglass is to be constructed such that the scale is uniform.
That is, the ratio of height difference between the level of water at two time instants to the time difference is a constant.


Your task is to find the mathematical equation the glass follows.. ie, report d log z / d log r accurate upto 3 decimal places at the judge.
Assume the hole to be infinitessimally small.
Also assume negligibe change in air pressure.

Inductor anyone?

A solenoid of self-inductance L, is allowed to reach steady state by connecting to a battery of emf E and internal resistance R.

Now, a soft iron core is quickly inserted in the solenoid such that the coefficient of self inductance changes from L to nL.

Determine the current in the circuit at the time of complete insertion.

Hollow or Solid

Petr has 2 rigid bodies 'A' and 'B': one is a hollow cylinder, the other solid. He allows them to roll (from rest) from the top of a circular track.

'A' displaces by an angle 'Qa' before losing contact with the track. 'B' displaces by 'Qb'. Also Qa>Qb.

Which is which?

Mechanics:

A small ring is located near one end of a rod. Next, the rod is given an angular velocity 'w' along the axis shown.

With what kinetic energy does the ring leave the rod?
Mass of ring='m'. Mass of rod='M'. Length of rod='L'.

The action takes place in a horizontal plane.

Poll:

Please vote here.

Kinematics:

Till yesterday, I thought these problems were difficult:

Find 'x' so that the 2 particles collide.