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Analog to Biot-Savart for E field
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[QUOTE="Gene Naden, post: 6004038, member: 640664"] ##\nabla \cdot E=\frac{1}{\epsilon}\rho## Gauss's law ##E=\frac{1}{4\pi\epsilon}\int \frac{(\nabla \cdot E) \hat r}{r^2} d \tau## Use the identity ##A \times (B \times C) = B (A \cdot C)-C(A\cdot B)## where ##A=\nabla##, and possibly integrate by parts, I am not sure, You get an an integral like ##\frac{1}{4\pi}\int \frac{(\nabla \times E) \times \hat r}{r^2} d\tau##. Use Maxwell's equation ##\nabla \times E = -\frac {\partial B}{\partial t}##. This gives you ##E=-\frac {1}{4\pi} \int \frac {(\frac {\partial B}{\partial t}) \times \hat r}{r^2} d\tau## Since you are integrating over space and not time, we can move the partial derivative out of the integral, getting ##E=-\frac {1}{4\pi} \frac{\partial}{\partial t} \int \frac { B \times \hat r}{r^2} d\tau## I hope this helps. [/QUOTE]
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Analog to Biot-Savart for E field
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