Consider a uniform charge distribution with charge density of `2C/m^(3)` throughout in space.If a Gaussian sphere has a variable radius which changes at the rate of 2m/s then value of rate of change of flux is proportional to `r^(k)`(r= radius of sphere).Then find the value of k .

If the surface area of a sphere of radius ris increasing uniformly at the rate 8((cm)^(2))/(s), then the rate of change of its volume is:

The rate of change of surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to

Find the rate of change of volume of a sphere with respect to its radius when r=4cm

A solid of radius 'R' is uniformly charged with charge density rho in its volume. A spherical cavity of radius R/2 is made in the sphere as shown in the figure. Find the electric potential at the centre of the sphere.

If the rate of change of surface area of a sphere is 4m^2 /sec , then the rate of change of volume when the radius is 3m is.

If V denotes the volume and S is the surface area of a sphere. If radius of sphere is 2 cm, then the rate of change of V w.r.t. S is

Find the average rate of change of the area of a circle with respect to its radius r as r changed from (i) 2 to 3

The volume of sphere is given by V=(4)/(3) pi R^(3) where R is the radius of sphere. Find the rate of change of volume with respect to R.

[" A solid sphere of radius "R" is charged with "],[" volume charge density "rho=Kr^(n)," where "K" and "n],[" are constants and "r" is the distance from its "],[" centre.If electric field inside the sphere at "],[" distance "r" is proportional to "r^(4)," then find the "],[" value of "n.]