To determine the separation distance between the two charged spheres, we can use Coulomb's Law, which is given by:

$F = k \frac{|q_1 q_2|}{r^2}$

Where:

• $F$ is the force between the charges (given as $7.0 \times 10^{-2}$ N),
• $k$ is Coulomb's constant, $k = 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2$,
• $q_1$ and $q_2$ are the charges of the spheres (given as $q_1 = 6.00 \times 10^{-6}$ C and $q_2 = -5.0 \times 10^{-6}$ C),
• $r$ is the separation distance between the charges (this is what we are solving for).

Rearranging the equation to solve for $r$:

$r = \sqrt{\frac{k |q_1 q_2|}{F}}$

Substitute the known values:

$r = \sqrt{\frac{(8.99 \times 10^9) \times (6.00 \times 10^{-6}) \times (5.0 \times 10^{-6})}{7.0 \times 10^{-2}}}$

Now let's calculate:

$r = \sqrt{\frac{(8.99 \times 10^9) \times (30.0 \times 10^{-12})}{7.0 \times 10^{-2}}}$

$r = \sqrt{\frac{269.7 \times 10^{-3}}{7.0 \times 10^{-2}}}$

$r = \sqrt{3.856 \, \text{m}^2}$

$r \approx 1.96 \, \text{m}$

Thus, the separation distance between the two objects is approximately 1.96 m.

The correct answer is B. 1.96 m.

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Would you like more details on Coulomb's Law or any other questions? Here are a few related topics to explore:

1. What is the relationship between Coulomb's Law and electric fields?
2. How does Coulomb's Law explain the attraction and repulsion between charged objects?
3. How does the magnitude of charge affect the force between two objects?
4. What are the units of electric charge and how are they defined?
5. How can Coulomb's Law be applied in different contexts like electrostatics and capacitors?

Tip: When using Coulomb's Law, always ensure that the charges are in Coulombs and the distance is in meters to maintain consistent SI units.