## Coulomb's Law, Electric Field and Superposition

A bead of charge +Q and another of charge +4Q are fixed a distance D apart. Is there a point between them where the electric field is zero? Is there any other point where the electric field is zero?Imagine we place a charge of one coulomb on the line joining the two charges – then the force acting on this charge (in Newtons) will be equal to the electric field (in Newtons/Coulomb). Clearly, the two forces (from the two charges) the test charge experiences will oppose each other in the area, so it is likely that there is a point (a distance x away from the +Q charge) where they have the same magnitude and exactly cancel.

- F=kQ*1/x

^{2}= k*4Q*1/(D-x)

^{2}

- 1/x

^{2}= 4/(D-x)

^{2}

x^{2} = (D-x)^{2}/4

x = (D-x)/2

x = D/3

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