Problem 1 (25 pts) point charge of 3.00 |/C is located in the center of a spheri

Question

Problem 1 (25 pts) point charge of 3.00 |/C is located in the center of a spherical cavity of radius 6. cm nside a spherical charged solid with 11 cm radius A (10 pts) Calculate the magnitude of the electric field inside the sphere at a distance 9. cm from the center of the cavity if it is insulating with the charge density distribution in the solid = 7× 10-4 C/m? CR. B. (5 pts) What is the electric field at the same point (r-g cm, inside the sphere) if the sphere is conductive and has the same total charge. (Sketch the charge distribution) c (5 pts) Calculate the electric force acting on charge of 5. JC placed at a distance 15 cm from the center (outside the solid) D (5 pts) For the section C, will your answer be different if the sphere is conductive or not. Why?

Explanation / Answer

(A) from Gauss law,

E ( 4 pi r^2) = Qin / e0

Qin = (3 x 10^-6) + (7 x 10^-4 x 4 x pi (0.09^3 - 0.06^3) / 3)

Qin = 4.504 x 10^-6 C

E = (4.504 x 10^-6) / (4 pi x 8.854 x 10^-12)(0.09^2)

E = 5 x 10^6 N/C

(B) E = 0

(C) Qin = (3 x 10^-6) + (7 x 10^-4 x 4 x pi (0.11^3 - 0.06^3) / 3)

Qin = 6.27 x 10^-6 C

E = (6.27 x 10^-6) / (4 pi x 8.854 x 10^-12)(0.15^2)

E = 2.504 x 10^6 N/C

F = q E = 12.52 N

(D) for r > R

Qin will be same. so E will also be same/

hence F = 12.52 N

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