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March Problem Lists

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

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...

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...