Sandbox testing.
$$ h(t)\nabla \times \tilde {\mathbf H} = \mathbf J +\epsilon_0 \dot {e}(t) \tilde {\mathbf E} $$
$$ h(t)\nabla \times \tilde {\mathbf H} = \mathbf J +\epsilon_0 \dot {e}(t) \tilde {\mathbf E} \tag{1}$$
$$ h(t)\nabla \times \tilde {\mathbf H} = \mathbf J +\epsilon_0 \dot {e}(t) \tilde {\mathbf E} \tag{1}\label{1}$$