Question

A point charge of 4 µC is located at x = -3.0 cm, and a second point charge of -14 µC is located at x = +4.0 cm. Where should a third charge of +6.0 µC be placed so that the electric field at x = 0 is zero.

Answer 1

the electric field originated by a number of charges is calculated by:
\[E=\frac{ 1 }{ 4 \times \pi \times \epsilon0} \times \sum_{1}^{i}\frac{ q _{i} }{ (r _{i})² }\]

If you
\[E=\frac{ 1 }{ 4 \times \pi \times \epsilon0} \times [\frac{ 4\times10^{-9} }{ 0,03² } + \frac{ -14\times10^{-9} }{ 0,04² } +\frac{ 6\times10^{-9} }{x² }] =0 \]

You should end up with the same absolute value but symmetrical positions, on the x axle.
You should confirm which one, summed to the q1=4x10⁻⁹ C, is equal to q3=-14x10⁻⁹C.

For my calculations,I've obtained x=0,037m or 3,7 cm.

Answer 2

sorry for my mistake.
nano Coulomb's are 10⁻⁶ and not 10⁻⁹.
please make the proper corrections.

Answer 3

this may be a silly question, but how do i determine where the x value is obtained? Do i do this through the graphing calculator somehow? Thanks!