Answer:
Explanation:
Electrostatic force is the product of the charges over the square of the distances.
F = kQq/d²
to have no net force on the middle charge, the forces with the outside charges must balance
k(5.3)(2.2)/x² = k(5.3)(8.2)/(L - x)²
(2.2)/x² = (8.2)/(L - x)²
(2.2)(L - x)² = (8.2)x²
(2.2)(L² - 2xL + x²) = (8.2)x²
2.2L² - 4.4xL + 2.2x² = 8.2x²
0 = 6.0x² + 4.4xL - 2.2L²
x = (-4.4L ±√((4.4L)² - 4(6.0)(-2.2L²))) / (2(6.0))
x = (-4.4L ±√(72.16L²)) / 12
x = (-4.4L ± 8.49L)) / 12
only the positive dimension makes sense
x = (-4.4L + 8.49L)) / 12
x = 4.09L / 12
x/L = 0.341225352...
x/L = 0.34
