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$\newcommand{\Tca}{\mathcal T}\newcommand{\Pca}{\mathcal P}$
There is energy momentum conservation law for the electromagnetic fields and an equation of continuity holds for it. Talking about momentum conservation, the electromagnetic field carries momentum \(\vec \Pca \) which is conserved for free fields. \begin{equation} \vec \Pca = \sqrt{\epsilon_0\mu_0} \,\vec S, \end{equation} where \(\vec S= (1/\mu_0) (\vec E \times \vec B)\) is the Poynting vector. The conservation law for the momentum takes the form
\begin{equation} \frac{\partial \Pca_j}{\partial t} + \nabla_k\cdot \Tca_{jk}=0, \quad k=1,2,3. \end{equation}
Here \(\Tca_{jk}\), are space components of the energy momentum tensor of the electromagnetic field, and are given by \begin{equation} \Tca_{jk}= \epsilon_0\Big(E_jE_k-\frac{1}{2}\delta_{jk} E^2\Big) + \frac{1}{\mu_0}\Big(B_jB_k -\frac{1}{2}B_jB_k\Big) \end{equation} Recalling that the current \(\vec J\) in the continuity equation, gives the flow of charge per unit area across a surface. The rate of flow of charge across a surface element \(\Delta S\), normal \(\hat n\), is given by \(\vec J \cdot \hat n \Delta S\). \\ Applying the same interpretation to the continuity equation for the e.m. field momentum, we see that \(n_k \Tca_{jk}\Delta S\) gives the transfer of momentum across the surface element \(\Delta S\) and hence the \(j^\text{th}\) component of the force on the surface element. If we integrate this quantity over a surface \(S\), we would get the force exerted by the electromagnetic waves on the surface \(S\). The tensor \(\Tca_jk\) is called {\tt stress tensor} as it gives force per unit area, or the stress, acting on a surface in the \(j^\text{th}\) direction. A similar discussion can be given for conservation of angular momentum.
