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### 5.1 Analogies between Electric fields and Gravitational fields

Gravitational Fields and Electric fields are analogous in their forms. In the below table is shown the analogous characteristics,

 Electric Field Gravitational Field Origin of Force Charge $Q$ Mass $m$ Force Law Coulomb’s Law, Newton’s Law of Gravitation, $$F_{e}=\frac{Qq}{4\pi \epsilon_{0}r^{2}}$$ $F_{g}=G\frac{Mm}{r^{2}}$ Definition of Field Strength Force acting per unit positive charge. Force acting per unit mass. $$E_{e}=\frac{Q}{4\pi \epsilon_{0}r^{2}}$$ $$g=G\frac{M}{r^{2}}$$ Definition of Potential Work done in bringing unit positive charge from infinity to the point. $$V=\frac{1}{4\pi \epsilon_{0}}\frac{Q}{r}$$ Work done in bringing unit mass from infinity to the point. $$\Phi=-G\frac{M}{r}$$ Change in Potential energy $$E_{p}=q\Delta V$$ $$E_{p}=m\Delta \Phi$$

**It is very important to realize that although the two fields have analogous form, the forces between the charged particle is way to stronger than that between the gravitational attraction between two charged particle due to their masses. Hence, in all practical electric calculations the gravitational attraction between them is ignored.