Physics Vidyapith ✍️

Electric field intensity at different points in the field due to uniformly charged thick hollow non-conducting sphere: Let us consider, A hollow non-conducting sphere of inner radius $r_{1}$ and outer radius $r_{2}$ in which $+q$ charge is evenly distributed evenly in the entire volume of the sphere. If $\rho$ is the volume charge density then electric field intensity at different points on the electric field of the thick hollow non-conducting sphere: Electric field intensity outside the thick hollow non-conducting sphere Electric field intensity on the surface of the thick hollow non-conducting sphere Electric field intensity at an internal point of the non-thick hollow conducting sphere 1. Electric field intensity outside the thick hollow non-conducting sphere: Let us consider, A point $P$ is outside the sphere which is at a $r$ distance from the center point $O$ of the sphere. The direction of electric flux is radially outward in the sphere. So the

Electromagnetic Wave: An electromagnetic wave is the combined effect of an electric field and magnetic field which carry energy from one place to another. When an electric field and the magnetic field are applied perpendicular to each other then a wave propagates perpendicular to both the electric field and the magnetic field. This wave is called the electromagnetic wave. Characteristics of Electromagnetic Wave: 1.) Electric and Magnetic Fields: Electromagnetic waves are produced through the mutually perpendicular interaction of electric and magnetic fields. The propagation of the wave is also perpendicular to both the electric field and the magnetic field. 2.) Wave Nature of electromagnetic waves: Electromagnetic waves are characterized by their wave-like behavior, so they exhibit the properties such as wavelength, frequency, amplitude, and velocity. This wave-like behavior of electromagnetic waves can undergo phenomena like interference, diffraction, and polarization. 3.

In electromagnetic waves, the electric field vector and magnetic field vector are mutually perpendicular to each other (Proof) The general solution of the wave equation for the electric field vector and magnetic field vector are respectively given below $\overrightarrow{E}= E_{\circ} e^{i(\overrightarrow{k}. \overrightarrow{r} - \omega t)} \qquad(1)$ $\overrightarrow{B}= B_{\circ} e^{i(\overrightarrow{k}. \overrightarrow{r} - \omega t)} \qquad(2)$ Here $E_{\circ}$ and $B_{\circ}$ are the complex amplitude of electric field vector $\overrightarrow{E}$ and magnetic field vector $\overrightarrow{B}$ respectively and $\overrightarrow{k}$ is the propagation constant. Now $\overrightarrow{\nabla} \times \overrightarrow{E}= \left( \hat{i} \frac{\partial}{\partial x} + \hat{i} \frac{\partial}{\partial x} +\hat{i} \frac{\partial}{\partial x} \right). \left( \hat{i}E_{x} + \hat{j}E_{y} + \hat{k}E_{z} \right) $ $\overrightarrow{\nabla} \times \overrightarrow{E}

Electromagnetic waves are transverse in nature: (Proof) The general solution of the wave equation for the electric field and magnetic field are respectively given below $\overrightarrow{E}= E_{\circ} e^{i(\overrightarrow{k}. \overrightarrow{r} - \omega t)} \qquad(1)$ $\overrightarrow{B}= B_{\circ} e^{i(\overrightarrow{k}. \overrightarrow{r} - \omega t)} \qquad(2)$ Here $E_{\circ}$ and $B_{\circ}$ are the complex amplitude of electric field vector $\overrightarrow{E}$ and magnetic field vector $\overrightarrow{B}$ respectively and $\overrightarrow{k}$ is the propagation constant. Now $\overrightarrow{\nabla}. \overrightarrow{E}= \left( \hat{i} \frac{\partial}{\partial x} + \hat{i} \frac{\partial}{\partial x} +\hat{i} \frac{\partial}{\partial x} \right). \left( \hat{i}E_{x} + \hat{j}E_{y} + \hat{k}E_{z} \right) $ $\overrightarrow{\nabla}. \overrightarrow{E}= \frac{\partial}{\partial x} \left(E_{x} \right)+ \frac{\partial}{\partial y} \left(E_{y} \rig

Diamagnetic Substances : Those substances, which are placed in the external magnetic field then they weakly magnetize in the opposite direction of the external magnetic field, are called diamagnetic substances. The susceptibility $\chi_{m} $ of diamagnetic substances is small and negative. Further, When diamagnetic substance placed in magnetic field then the flux density of the diamagnetic substance is slightly less than that in the free space. Thus, the relative permeability of diamagnetic substance $\mu_{r}$, is slightly less than 1. Properties of Diamagnetic substances: 1. When a rod of a diamagnetic material is suspended freely between external magnetic poles (i.e. Between North and South Poles) then its axis becomes perpendicular to the external magnetic field $B$ (Figure). The poles produced on the two sides of the rod are similar to the poles of the external magnetic field. 2. In a non-uniform magnetic field, a diamagnetic substance tends to move from the stronge