A uniform metal sphere of radius α and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4α (figure 11-E2). The Centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P₁ and P₂ shown in the figure.

Question

Philoid · Accepted Answer

Here the point P₁ lies outside the sphere but inside the shell. We know the electric field inside the shell is zero. Therefore, only the sphere gives rise to the field.

The distance of P₁ from the center of the sphere is x=4a -a +a = 4a

Therefore, electric field

Field at P₂ is due to both the sphere and the shell.

The distance of from the center of the sphere is x = 4a+a+a = 6a.

Therefore, the field is

The distance of from the center of the sphere is x = 4a+a= 5a.

Therefore, the field is

The total electric field is thus

A uniform metal sphere of radius α and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4α (figure 11-E2). The Centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P1 and P2 shown in the figure.

A uniform metal sphere of radius α and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4α (figure 11-E2). The Centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P₁ and P₂ shown in the figure.