Two thin, isolated, concentric conducting spheres of radii 2.60 cm and 10.10 cm

Question

Two thin, isolated, concentric conducting spheres of radii 2.60 cm and 10.10 cm, have net charges of 46.50 nC and 18.00 nC, respectively. What is the electric field at 1.690 cm from the center of the spheres? Use the sign of the field to indicate direction, thus a positive electric field would point away from the center of the spheres.

What is the electric potential at 1.690 cm from the center of the spheres?

What is the electric field at 5.975 cm from the center of the spheres?

What is the electric potential at 5.975 cm from the center of the spheres?

What is the electric field at 11.790 cm from the center of the spheres?

What is the electric potential at 11.79 cm from the center of the spheres?

Explanation / Answer

a)Electric field is 0 in both cases since it is inside the sphere in each case.

b)V1=kQ1/R1=9*10^9*46.5*10^-9/0.026=16096V

V2=kQ2/R2=9*10^9*18*10^-9/0.101=1604V

c)E1=kq1/r^2=9*10^9*46.5*10^-9/0.05975^2=117225N/C

E2=0 (since it is inside the sphere)

d)V1=kQ1/r=9*10^9*46.5*10^-9/0.05975=7004V

V2=kQ2/R2=9*10^9*18*10^-9/0.101=1604V

e)E1=kq1/r^2=9*10^9*46.5*10^-9/0.1179^2=30107N/C

E2=kq2/r^2=9*10^9*18*10^-9/0.1179^2=11654N/C

f)V1=kq1/r1=9*10^9*46.5*10^-9/0.1179=3550V

V2=kq2/r2=9*10^9*18*10^-9/0.1179=1374V

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