N spherical droplets , each of radius r have been charged to have a potential V each.If all these droplets were to coalece to form a single large drop what would be the potential of this large drop?
(Given taht the capacitance of a sphere of radius x equals 4pie absilon not Kx)

Asked by vasturushi | 27th Dec, 2017, 09:17: PM

Expert Answer:

let q be the charge on each spherical capacitor.
capacitance of each droplet = 4πε0Kr = q / V;
where r is radius of each drop, V is potential on each drop
 
hence V = q / 4πε0Kr
 
volume of coaleced spheren fromed from N droplets = N × (4/3) π×r3;
 
hence radius of coalesed sphere = N1/3×r
capacitance of coalesed sphere = 4πε0KN1/3×r
 
potential =charge/capacitance =( N×q ) / ( 4πε0KN1/3×r ) = ( N2/3 × q ) / ( 4πε0Kr ) = N2/3 V  

Answered by  | 28th Dec, 2017, 04:57: PM