Find the resulting electric field at 7 cm and 10 cm from the center of a sphere having two shells.

Question

Two thin, spherical, concentric metal shells have a radius of 6 cm and 8 cm. The inner shell carries a charge of 7 nC and the outer shell carries a charge of 4 nC. Find the resulting electric field at a) 7 cm from the centre; b) 10 cm from the centre.

The answers are 1.29 x 10^4 N/C and -38.6 N*m^2/C but I'm not sure how they got them.

Answer 1

Use Gauss's Law E(4πr²) = Q_enc/ε₀ for spherically symmetry (ε₀ = 8.85 x 10^-12 in MKS) or jus E = k_eQ_enc/r²

a) r = .07 m Q_enc = 7 x 10^-9 C

b) r - .1 m Q_enc = 11 x 10^-9 C

a) gets correct answer

b) The answer has the wrong units and can't be negative given the problem.