In this post, let's learn about the multipole expansion of a potential with the help of a beautiful problem and find the constant.
In this post, let's learn about the multipole expansion of a potential with the help of a beautiful problem and find the constant.
TIFR 2015 Problem 7 Solution is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate program leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects. The image is a front […]
Let's learn the inductance of a toroid with the help of a beautiful problem. Show that the inductance of a toroid of rectangular cross-section is given by..
TIFR 2015 Problem 4 Solution is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate programme leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects. The image is a front […]
We have indicated the source of these problems. Do not look up solutions. It is fun to try it yourself or see others try them live! Let P be an interior point of triangle ABC and AP, BP, CP meet the sides BC, CA, AB in D, E, F respectively. Show that \( \frac{AP}{PD}=\frac{AF}{FB}+\frac{AE}{EC} \) […]
The brightest meteor shower of the year is here! From December 14th to 17th, look at the North-Eastern sky above the Gemini constellation. (It won't be prominent in Southern Hemisphere, so our students in Singapore and Australia will miss it). In India, try moving to a less polluted region (and also out of the glare zone […]
Claim: If G has no subgroups H /= (e), G, then G must be cyclic of prime order. Proof: One Line Proof: If the order of G is composite, then it has Sylow Subgroups. More than one Line Proof: If the order of G is composite then there exists d that divides |G| and 1 < d < |G|. […]
TIFR 2015 Problem 3 Solution is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate programme leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects. The image is a front […]
TIFR 2015 Problem 2 Solution is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate programme leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects. The image is a front […]
Sine of an angle, half chord and vertical projection Note that half chord corresponding to a half arc is same as the magnitude of vertical projection.