A hollow metal sphere has inner and outer radii of 20.0 cm and 30.0 cm, respecti

Question

A hollow metal sphere has inner and outer radii of 20.0 cm and 30.0 cm, respectively. As shown in the figure, a solid metal sphere of radius 10.0 cm is located at the center of the hollow sphere. The electric field at a point P, a distance of 15.0 cm from the center, is found to be E1 = 2.11

A hollow metal sphere has inner and outer radii of 20.0 cm and 30.0 cm, respectively. As shown in the figure, a solid metal sphere of radius 10.0 cm is located at the center of the hollow sphere. The electric field at a point P, a distance of 15.0 cm from the center, is found to be E1 = 2.11 middot 104 N/C, directed radially inward. At point Q, a distance of 35.0 cm from the center, the electric field is found to be E2 = 2.11 middot 104 N/C, directed radially outward. Determine the total charge on the surface of the inner sphere. Determine the total charge on the surface of the inner surface of the hollow sphere. Determine the total charge on the surface of the outer surface of the hollow sphere.

Explanation / Answer

the field at 15 cm is due to the charge on the inner sphere of radius 10 cm. And that has to be negative in nature as the field is inwards
Now the field at 35 is due to algebraic sum of charges (all the three)
If Q1 is the negative charge then E1 = K * Q1 /(0.15)^2
If Q is the total then E2 = K Q / (0.35)^2
Now being equal we get Q / Q1 = (0.15/0.35)^2
Right from E1 you could find Q1 and from above you can get Q.
But Q = Q1 + Q2 + Q3
Now Q2 + Q3 could be got. But you have to think so deep to find Q2 and Q3. All the best dear
Note: By Gauss's theorem field inside a charged sphere is 0
Field due to charged sphere is the same as if the charge is concentrated at the center.

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