'N' small drop of same size are charge to 'V' volt each if they combine to form single large drop then what will be the realation between Qq,Vv,Rr?
The relation between Q (charge), V (voltage), and R (radius) for a single charged drop is given by the equation:
Q = 4πεR^2V,
where ε is the permittivity of the medium.
To find the relation between the values of Q, V, and R when N small drops combine to form a single large drop, we need to consider how the charges and radii of these drops are related.
Let's denote the charge of each small drop as q and the radius as r. Since the size of each small drop is the same, we can assume that each drop has the same charge q and radius r.
The total charge of N small drops is given by the equation:
Q_total = Nq.
When these N small drops combine to form a single large drop, the total charge of the large drop will be the sum of the charges of the small drops:
Q_large = Q_total = Nq.
Similarly, the radius of the large drop will be the sum of the radii of the small drops:
R_large = N^(1/3) * r.
Now, we have the values of Q_large, V, and R_large for the single large drop. To find the relation between Q, V, and R, we substitute the values into the original equation:
Q_large = 4πεR_large^2V.
Substituting the values:
Nq = 4πε(N^(1/3) * r)^2V.
Simplifying this equation:
Nq = 4πεN^(2/3)r^2V.
Now, we can see the relationship between Q, V, and R for N small drops combining to form a single large drop:
Q = Nq,
V = V, and
R^2 = N^(2/3)r^2.
Therefore, the relation between Q, V, and R for N small drops combining to form a single large drop is:
Q = 4πεR^2V/N^(1/3).