Integrating the special electromagnetic characteristics of Synthetic Aperture Radar (SAR) in deep neural networks is essential in order to enhance the explainability and physics awareness of deep learning. In this paper, we firstly propose a novel physics guided and injected neural network for SAR image classification, which is mainly guided by explainable physics models and can be learned with very limited labeled data. The proposed framework comprises three parts: (1) generating physics guided signals using existing explainable models, (2) learning physics-aware features with physics guided network, and (3) injecting the physics-aware features adaptively to the conventional classification deep learning model for prediction. The prior knowledge, physical scattering characteristic of SAR in this paper, is injected into the deep neural network in the form of physics-aware features which is more conducive to understanding the semantic labels of SAR image patches. A hybrid Image-Physics SAR dataset format is proposed, and both Sentinel-1 and Gaofen-3 SAR data are taken for evaluation. The experimental results show that our proposed method substantially improve the classification performance compared with the counterpart data-driven CNN. Moreover, the guidance of explainable physics signals leads to explainability of physics-aware features and the physics consistency of features are also preserved in the predictions. We deem the proposed method would promote the development of physically explainable deep learning in SAR image interpretation field.