A total charge (q) is spread uniformly over the inner surface of a non-conducting hemispherical cup of inner radius (a). Calculate the electric field. Discussion: Consider a circular strip symmetric about (z-axis) of radius (r) and width (ad\theta) The charge on the strip is $$ dq=q\frac{2\pi r ad\theta}{2\pi a^2}=\frac{qr d\theta}{a}=q sin\theta d\theta$$ (a) At the […]
TIFR 2013 Problem 39 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 […]
If the electric potential is given by (\chi=cxy), calculate the electric field. Discussion: $$ E_x=-\frac{\partial\chi}{\partial x}=-cy$$ $$ E_y=\frac{\partial \chi}{\partial y}=-cx$$ Hence electric field $$ \vec{E}=-c(y\hat{i}+x\hat{j})$$
TIFR 2013 Problem 38 Solution has been written for TIFR entrace preparation series. A problem using the idea of eigenvector from Linear Algebra.
What is the maximum charge that can be given to a sphere of diameter (10cm) if the breakdown voltage of air is (2\times10^4 V/cm)? Discussion: Dielectric breakdown is when current flows through an electrical insulator when the voltage applied across it exceeds the breakdown voltage. This results in the insulator becoming electrically conductive. The breakdown voltage of air […]
Let's discuss a problem on Infinite Number of Charges from Physics Olympiad. Try the problem first, and then read the solution here.
Let's discuss a problem based on Checking irreducibility over \(\mathbb{R}\) from TIFR 2013, Problem 37. Try this Problem and then read the solution.
A pendulum bob of mass (80mg) carries a charge of (2*10^{-8}C) at rest in an horizontal uniform electric field of (20,000V/m ). Find the tension in the thread of the pendulum and the angle it makes with the vertical. Discussion: Electric force $$ F=qE=210^{-8}20,000=410^{-4}$$ Gravitational force $$ mg= 8010^{-6}9.8=7.8410^{-4}N$$ Balancing the horizontal and vertical components […]
Let's learn to check injectivity with the help a problem from TIFR 2013 problem 36. Try it yourself first, then read the solution here.
Find the flux through a spherical Gaussian surface of radius (a=1m) surrounding a charge of (8.85pC). Solution: The value of (\epsilon_0=8.85*10^{-12}) The flux through the Gaussian surface is the charge (Q) located inside the surface. Therefore, $$ \Phi=\frac{Q}{\epsilon_0}$$ $$=8.8510^{-12}/8.8510^{-12}$$ $$=1Nm^2/C$$