© All Rights reserved @ LearnWithDash
Step-by-Step Solution
Step 1: Identify the initial charges on the spheres
Two identical conducting spheres carry charges of 2.1 nC and −0.1 nC. Since they are identical and have negligible volume, they will share their total charge equally upon contact.
Step 2: Calculate the net charge and the final distribution
The total charge before contact is:
Q_{\text{total}} = 2.1\,\text{nC} + (-0.1\,\text{nC}) = 2.0\,\text{nC}.
When brought into contact, this total charge is shared equally between the two spheres. Hence, each sphere gets:
Q_{\text{sphere}} = \frac{2.0\,\text{nC}}{2} = 1.0\,\text{nC}.
Step 3: Apply Coulomb’s Law
After they are separated by a distance of r = 0.5\,\text{m} , the electrostatic force between them is given by Coulomb’s Law:
F = \frac{1}{4 \pi \varepsilon_0} \times \frac{q_1\,q_2}{r^2}.
Using q_1 = 1.0 \times 10^{-9}\,\text{C},\, q_2 = 1.0 \times 10^{-9}\,\text{C},\, r = 0.5\,\text{m}, and
\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9\,\text{N\,m}^2\,\text{C}^{-2},
we get:
F = (9 \times 10^9) \times \frac{ (1.0 \times 10^{-9}) \times (1.0 \times 10^{-9}) }{ (0.5)^2 }.
Step 4: Simplify the expression
F = (9 \times 10^9) \times \frac{1.0 \times 10^{-18}}{ 0.25 }
= (9 \times 10^9) \times (1.0 \times 10^{-18}) \times \frac{1}{0.25}.
\frac{1}{0.25} = 4,
so
F = 9 \times 10^9 \times 1.0 \times 10^{-18} \times 4 = 36 \times 10^{-9}\,\text{N}.
Step 5: State the final answer
The electrostatic force acting between the spheres is
36 \times 10^{-9}\,\text{N}.
