March Problem Lists

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Understand Choose your course and download the Problem List document. The assignment page link is also added. You may submit the solutions there. This will constitute 50% of your monthly grade. Math Olympiad Early Bird (India) Number Theory Problem List (Early Bird)...

Multipole Expansion of a Potential

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Q. An insulating rod running from \(z=-a to z=a\) carries indicated line charges. Determine the leading term in the multipole expansion of the potential is given by $$ \lambda=kcos(\frac{\pi z}{2a})$$ where k is a constant. Solution: Potential due to multipole...

Inductance of a Toroid

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Show that the inductance of a toroid of rectangular cross-section is given by $$ L=\frac{\mu_0N^2Hln(b/a)}{2\pi}$$ where \(N\) is the total number of turns, \(a\) is the inner radius, \(b\) is the outside radius and \(H\) is the height of the toroid. Solution: Using...

Degrees of Freedom for Gas Molecules

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When a gas expands adiabatically, its volume is doubled while its absolute temperature is decreased by a factor \(1.32\). Compute the number of degrees of freedom for the gas molecules. Solution: The number of degrees can be found from the relation $$...

Efficiency of Heat Engine

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A heat engine absorbs heat of \(10^5Kcal\) from a source, which is at \(127^\circ\) and rejects a part of heat to sink at \(27^\circ\). Calculate the efficiency of the engine and the work done by it. Solution: The efficiency of the engine is $$...

Magnetic Field at the Centre of a Ring

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A ring of radius \(R\) carries a linear charge density \(\lambda\). It is rotating with angular speed \(\omega\). What is the magnetic field at the centre? Discussion: Linear charge density $$ \lambda=\frac{Q}{2\pi R} $$ When the ring is rotated about the axis, the...