If we have some steady current flowing in space (hypothetical model) with density $\mathbf J$ then the magnetic field at any point in space is $$\mathbf B = \frac{\mu_0}{4\pi} \int \frac {\mathbf J \times \mathcal {\hat r} }{\mathcal {r}^2} dV$$ and we know that the the curl of magnetic field cre...

Now suppose a magnetic field is increasing inwards and we keep a loop of radius $r_B$ as shown in picture. then the magnetic field at point A is given $E_A=(r_B/2)*(dB/dt)$ Now if i keep a small loop of radius $r_s$ such that $r_s<r_B$ as shown in figure . Note small loop is kept independent ...

I am trying to figure out how the famous three matrices are obtained: \begin{equation} T_1=\begin{pmatrix} 0&0&0\\0&0&-i\\0&i&0\end{pmatrix} \end{equation} \begin{equation} T_2=\begin{pmatrix} 0&0&i\\0&0&0\\-i&0&0\end{pmatrix} \end{equation} \begin{equation} T_2=\begin{pmatrix} 0&-i&0\\i&0&0\\0&0&...

Now suppose a magnetic field is increasing inwards and we keep a loop of radius $r_B$ as shown in picture. $∮E•dl= dφ/dt$ which means $E(2πr_B)=(π(r_B)²)*(dB/dt)$(as electric field is uniform) Now it is questioned that why electric field induced should be uniform.The only answer to this that i ...