Arturo O. answered • 05/19/18

Tutor

5.0
(66)
Experienced Physics Teacher for Physics Tutoring

At the point x where the field is zero, the fields from the 2 source charges must be equal and opposite, so their magnitudes must the same.

(E1): k|q

_{1}|/(x - x_{1})^{2}= k|q_{2}|/(x - x_{2})^{2}|q

_{1}| = 6.4 μC|q

_{2}| = 1.6 μCx

_{1}= -4.0x

_{2}= 0Plug into equation (E1) and simplify.

6.4/(x + 4)

^{2}= 1.6/x^{2}x

^{2}+ 8x + 16 = 4x^{2}-3x

^{2}+ 8x + 16 = 0x = 4m

or

x ≅ -1.33 m

Note that a solution of -1.33 m is not physically possible, since that would place the test charge in between 2 source charges of opposite signs, which will always result in a net electric force on the test charge. Therefore, the only solution must be

x = 4m.