Answer:
Explanation:
For the first case , the expression for electrostatic force can be given by the following .
F = K x 8Q x 2Q / r² where k is a constant .
F = K 16 Q² / r²
When they touch , some charge is neutralized . Net charge remaining
= 8Q - 2 Q = 6 Q
Charge on each sphere = 6Q/2 = 3 Q .
Force between them
F₁ = k 3Q x 3 Q / r² = k 9 Q² / r²
F₁ / F = 9 / 16
F₁ = 9 F / 16 .
The new force on each sphere will be "[tex]\frac{9}{16} F[/tex]".
We have,
Now,
The initial force between them will be:
→ [tex]|\vec{F}| = \frac{1}{4 \pi \epsilon_0 } \frac{Q_1 Q_2}{r^2}[/tex]
[tex]= \frac{1}{4 \pi \epsilon_0 } \frac{8Q\times (2Q)}{r^2}[/tex]
[tex]= \frac{16 Q^2}{4 \pi \epsilon r^2}[/tex]
When the separated, the charge on each become
→ [tex]Q'= \frac{Q_1+Q_2}{2}[/tex]
[tex]= \frac{+8Q-2Q}{2}[/tex]
[tex]= \frac{6Q}{2}[/tex]
[tex]= 3Q[/tex]
For "Q" between them,
→ [tex]F' = \frac{1}{4 \pi \epsilon_0 } \frac{Q'\times Q'}{r^2}[/tex]
[tex]= \frac{1}{4 \pi \epsilon_0 }\frac{3Q\times 3Q}{r^2}[/tex]
[tex]= \frac{1}{4 \pi \epsilon_0} \frac{9Q^2}{r^2}[/tex]
hence,
The new force will be:
→ [tex]\frac{F'}{F} = \frac{1}{4 \pi \epsilon_0} \frac{9 Q^2}{r^2}\times \frac{4 \pi \epsilon r^2}{16 Q^2}[/tex]
[tex]= \frac{9}{16}[/tex]
[tex]F' = \frac{9}{16} F[/tex]
Thus the above answer is correct.
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