Question

Problem 3: There are 5 conducting spheres with radii of 5cm, 10cm, 15cm, 20cm, and 25cm, arranged concentrically so that their centers overlap. Each sphere has a net charge of -20mC. A: Use Gauss's law to find the electric field inside the inner sphere, between each of the spheres, and outside of the outer sphere. B: What is the charge density on the outer surface of each of the conducting spheres? C: If a conducting wire was electrically connected through all 5 spheres, what would be the new charge density for each sphere, if it changes?

Answer 1

ANSWER:

Given that, These are 5 conducting spheres with jad; of 5cm , 10cm, 15cm, 20cm and 25cmi arranged concentesically (A) The electric field is seen to be identifical inside the sphere due to that point charge. Since all the charges will reside on the conducting Surface, so that a Gaussian Surface will be enclosed with no choorge ; and electric field will be zero at all point inside the Spherical conductors the field Outside oldes 5 Sphese is, The electric E- UTEM 2 - 5 anet Что я ден five conducting sphese is The net radius of the pet - 5cm tocm +150m + 20cm + 25cm . - 75cm Bierno). -0.75m

Substitute the values, to find electric field outside the outer 5 Conducting spheses is, come chose 47(8-853101c? 7.7°) (0.7500)? 20x10°c : -5 uale 85x10'2c%. N!m)(0.75m)? --122 10cin I DO X103 x 3x8 85x6 75 X 75 X10 - 100x10 3 G2-52525*10-12 - 1599x10 N/c. : -1.60x10 / surface of B) The change density on the outer each conducting sphere is, Elle P=E& Substiteite values, P=(-1-60x109/6) (6-85x10"c? Nim?) 3.-14.16 *10°C/m2 ~21.42x16 20c/m?

c) when the spherical conductors are connected toy a conducting coure, change is ged:Stouted in all the is spheres so that charge density coill become uniform thawuph the surface area of all the spheres.