Varying the Ricci tensor with respect to the metric $g^{\mu\nu}$, one would get $ \delta R_{\mu\nu} = \delta(g^{\rho\sigma} R_{\rho\mu\sigma\nu}) = g^{\rho\sigma}\delta R_{\rho\mu\sigma\nu} + \delta g^{\rho\sigma} R_{\rho\mu\sigma\nu}, $ but in all my references I found that $\delta R_{\mu\nu} ...

It is a general concept that horizontal forces can only influence physical quantities along horizontal direction; similarly vertical force can produce acceleration etc. only along vertical direction. This is the same concept that helps us study projectile motion as a combination of two independen...

As we know that the electric field between two parallel plates of a capacitor is $$E=\frac{\sigma}{\epsilon_0}$$, so the magnitude of force exerted by one plate on the other should have been $$F=QE$$. But in reality it is$$F=\frac{QE}{2}$$. How is that possible? Where have i mistaken? Also, I wo...

Suppose I have two plate electodes with a dielectric material between them with a permitivity of $\epsilon=10$. I now put a voltage V between them. What is the electric field in the dielectric region? Well since the electrodes are plates we have simply: $E = V/d$ which is independent of $\ep...