Question

A solid non-conducting sphere of radius R carries a charge Q distributed uniformly throughout its volume. At a radius r (r < R) from the center of the sphere the electric field has a value E. If the same charge Q were distributed uniformly throughout a sphere of radius 2R the magnitude of the electric field at a radius r would be equal to:__________

Answer 1

The electric field is E/8.

Step-by-step explanation:

The electric field due to a solid sphere of uniform charge density inside it is given by

`E =(\rho r)/(3)`

where,
`\rho` is the volume charge density and r is the distance from the center.

For case I:

`\rho = (Q)/((4)/(3)\pi R^3)`

So, electric field at a distance r is

`E = \frac { 3 Q r}{3* 4\pi R^3}\\\\E = (Q r)/(4\pi R^3)`

Case II:

`\rho = (Q)/((4)/(3)\pi 8R^3)`

So, the electric field at a distance r is

`E' = \frac { 3 Q r}{3* 32\pi R^3}\\\\E' = (Q r)/(8* 4\pi R^3)\\\\E' = (E)/(8)`

Answer 2

Hence the answer is E inside
`= KQr_(1) /R^(3)`.

Step-by-step explanation:

E inside
`= KQr_(1) /R^(3)`

so if r1 will be the same then

E
`\begin{bmatrix}Blank Equation\end{bmatrix}` proportional to 1/R3

so if R become 2R

E becomes 1/8 of the initial electric field.