A metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal spherical shell with radius rb. There is charge + q on the inner sphere and charge − q on the outer spherical shell as shown below. Take the potential V to be zero when the distance r from the center of the spheres is infinite.(Figure 1) Calculate the potential V(r) for r>rb. (Hint: The net potential is the sum of the potentials due to the individual spheres.) Use ϵ0 as the permittivity of free space and express your answer in terms of some or all of the variables r, ra, rb, q, and any appropriate constants.

A metal sphere with radius ra is supported on an insulating stand at the center of a hollow metal spherical shell with radius rb There is charge q on the inner class=

Respuesta :

The potential inside the inner sphere will be "0".

The inside sphere would be charged positively. Increased potential expressions ([tex]V_1[/tex]) because of the interior metal sphere, such as:

  • [tex]V_1 = \frac{kq}{r}[/tex]

The outer area sphere would be charged positively. Increased potential expressions ([tex]V_2[/tex]) because of the interior metal sphere, such as:

  • [tex]V_2 = \frac{k(-q)}{r}[/tex]

hence,

Throughout the inner sphere, the potential will be:

→ [tex]V = V_1+V_2[/tex]

By substituting the values, we get

→     [tex]= \frac{kq}{r} +(-\frac{kq}{r} )[/tex]

→     [tex]= \frac{kq}{r} -\frac{kq}{r}[/tex]

→     [tex]= 0[/tex]

Thus the answer above is right.  

Learn more:

https://brainly.com/question/16013743

Ver imagen Cricetus