Question

A thin-walled metal spherical shell of radius a = 1.80 cm has a charge qa = 8.00×10-6C. Concentric with it is a thin-walled metal spherical shell of radius b = 5.20 cm and charge qb = 2.50×10-6 C.

Find the electric field at distance r = 0 cm from the common center. Tries 0/10

Find the electric field at distance r = 3.70 cm from the common center. Tries 0/10

Find the electric field at distance r = 8.90 cm from the common center. Tries 0/10

Discuss the criterion one would use to determine how the charges are distributed on the inner and outer surface of the shells. What is the charge on the outer surface of the outer shell?

Answer 1

given

thin-walled metal spherical shell of radius a = 1.80 cm

= 0.018 m

of q_a = 8.00 x 10^-6 C

thin-walled metal spherical shell of radius b = 5.20 cm

= 0.052 m

of q_b = 2.50 x 10^-6 C

the electric field at distance r = 0 cm from the common center

E.dA = q / _o

q = 0

E.dA = 0

the electric field at distance r = 3.70 cm from the common center

E.dA = q / _o

E . A = q / _o

E x 4 r² = q / _o  

E = q_a / 4 _o r²

= 9 x 10⁹ x 8 x 10^-6 / ( 0.037² )

E = 5.259 x 10⁷ C/m²

the electric field at distance r = 8.90 cm from the common center

E.dA = q / _o  

E = ( q_a + q_b ) / 4 _o r²

= 9 x 10⁹ x ( 8 + 2.5 ) x 10^-6 / 0.0809²

E = 1.443 x 10⁷ C/m²

here the total charge on a shell is constant, and outer surface of outer charge is induced

so that total charge on shell is equally distributed that initially provided charge.