A solid metal sphere of radius a = 1.30 cm is surrounded by a concentric spheric

Question

A solid metal sphere of radius a = 1.30 cm is surrounded by a concentric spherical metal shell of inner radius b = 3.20 cm and outer radius c = 3.70 cm. The inner sphere has a net charge of Q1 = 4.70 ?C, and the outer spherical shell has a net charge of Q2 = -8.30 ?C.

a. What is the radial component of the electric field Er at a point located at radius r = 2.90 cm, i.e. between the two conductors? Er is positive if it points outward, negative if it points inward.

b. What is Er at a point located at radius r = 4.10 cm, i.e. outside the outer shell?

c. What is the surface charge density, ?b, on the inner surface of the outer spherical conductor?

d. What is the surface charge density, ?c, on the outer surface of the outer spherical conductor?

Explanation / Answer

Here ,

a) at r = 2.90 cm

field is due to inside charge only

electric field , E = k * Q1/r^2

E = 4.70 *10^-6 * 9*10^9/.029^2

E = 5.03 *10^7 N/C

the radial electric field is 5.03 *10^7 N/C

B)

outside the outer sphere ,

E = E = k * (Q1 + Q2)/r^2

E = (4.70 - 8.30) *10^-6 * 9*10^9/.029^2

E = -3.85 *10^7 N/C

the radial electric field is -3.85 *10^7 N/C

c)

on the inner surface ,

charge density = -Q1/(area)

charge density = -4.70 *10^-6/( 4 * pi*0.032^2)

charge density = - 3.65 *10^-4 C/m^2

the charge density on the inner surface is - 3.65 *10^-4 C/m^2

d)

on the outer surface ,

charge density = (Q2 + Q1)/(area)

charge density = (-8.30+ 4.70) *10^-6/( 4 * pi*0.037^2)

charge density = -2.09*10^-4 C/m^2

the charge density on the outer surface is -2.09*10^-4 C/m^2

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