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 Sci Advisor HW Helper PF Gold P: 2,026 The first two terms of Eq. (4) should be $$\mathbf{f} = \epsilon_0\left[ \boldsymbol{\nabla}\cdot( \mathbf{E}\mathbf{E}) + (\mathbf{E}\cdot\boldsymbol{\nabla}) \mathbf{E} \right]$$. Then use $$(\mathbf{E}\cdot\boldsymbol{\nabla}) \mathbf{E} =(1/2)\nabla({\bf E\cdot E })$$. Writing these two terms with indices gives Eq. (5). The other terms don't enter with no B field. dE/dt can't enter because this would imply a B field.