Question

Two identical spheres having charges $8\mu C$ and $-4\mu C$ are kept at a certain distance apart. Now they are brought into contact, after that again they are kept at the same distance. Compare the forces in the two cases

• A. $4:1$
• B. $12:1$
• C. $8:1$
• D. $16:1$

Answer 1

The correct option is C $8:1$

If two identical sphere having charge $8\mu C$ and $-4\mu C$ are kept a certain distance apart, then force between them is $F$.

Let the distance between charged sphere is $d$.

then, $F=\frac{k\times 8\times (-4)\times {10}^{-12}}{d^2}$ [attractive]

$d^2=\frac{32k\times {10}^{12}}{F}$ ....(i)

Now, when both the identical sphere touch, then charge on each sphere is average of initial charge on sphere.

i.e, $Q=\frac{(8-4)\mu C}{2}=2\mu C$ on each sphere.

Now, Force between them is:

$F^{\prime }=\frac{k\times (2\times {10}^{-6}{)}^2}{d^2}$

From equation (i), we get

$F^{\prime }=\frac{k\times 4\times {10}^{-12}\times F}{32k\times {10}^{-12}}$

$F^{\prime }=\frac{F}{8}$

so, the ratio is $8:1$