The static electric field inside a dielectric medium with relative permittivity εr = 2.25, expressed in cylindrical coordinate system is given by the following expression \(E = {a_r}\;2r + {a_\phi }\left( {\frac{3}{r}} \right) + {a_z}\;6\) Interpret the expression locally in a simply connected region with r > 0 that does not wrap around the z-axis.
9 ε0
For a homogeneous dielectric, free volume charge density is \(\rho_f=\nabla\cdot\mathbf D=\varepsilon\nabla\cdot\mathbf E\). Here \(\nabla\cdot\mathbf E=\frac1r\frac{\partial(2r^2)}{\partial r}=4\), so \(\rho_f=2.25\varepsilon_0(4)=9\varepsilon_0\). The 3/r azimuthal term is locally curl-free away from the axis, but would prevent a globally single-valued electrostatic potential on a region containing a complete encircling loop.
Important Questions from Electrostatics
A uniform ring charge of radius $R$ carries a total charge $Q$. Which one of the following options correctly quantifies the magnitude of the force on a point charge of strength $q$ kept at the center of the ring?
($\epsilon$ is the permittivity of the medium)
For a uniform line charge of 8 nc/m lying along the z axis, the electric field at a radius of 3 m from the uniform line is given by :
The current in a coil of inductance 5 H changes linearly from 10 A to 2 A in t seconds. If the induced emf is 40 V, what is the time t?
What are the materials which exhibit electric polarization even in the absence of an applied electrical field?
What is the relative permittivity of slate dielectric?
