## Multipole Expansion of a Potential

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

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... 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 $$... ## Efficiency of Heat Engine A heat engine absorbs heat of $$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

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...