CONCEPT:
- A capacitor is a device where two conductors are separated by an insulating medium that is used to store electrical energy or electrical charge
- The capacitance is defined as the ability to store charge or it is the number of charges stored per unit potential in a capacitor.
\(\Rightarrow C=\frac{Q}{V}\)
Where Q = Charge and V = Potential difference
- The potential on a charged sphere is given by
\(\Rightarrow V = \frac{K Q}{R}\)
Where K = Dielectric constant Q = Charge, R = Radius
CALCULATION:
Let r = radius after splitting, R = Radius before splitting
- The potential on a charged sphere is given by
\(\Rightarrow V = \frac{K Q}{R}\)
The above of the equation can be rewritten as
\(\Rightarrow \frac{Q}{V} = \frac{R}{K}\)
We know \(C=\frac{Q}{V}\), then the above equation can be written as
\(\Rightarrow C = \frac{R}{K}\)
As it is given that, C = 1 μF, then
\(\Rightarrow \frac{R}{K} = 1 \ \mu F\)
After splitting,
\(\Rightarrow 8\times (\frac{4}{3}\pi r^3)=\frac{4}{3}\pi R^3\)
\(\Rightarrow r=\frac{R}{2}\)
- The potential of the smallest drop is given by
\(\Rightarrow V = \frac{r}{K}\)
Substituting the value of r in the above equation
\(\Rightarrow V = \frac{R}{2 K}\)
The substituting the value of \(\frac{R}{K} = 1 \ \mu F\) in the above equation
\(\Rightarrow V = \frac{1}{2 }\mu F\)
Hence, option 1 is the answer