Two charged concentric spherical shells have radii 8.83 cm and 15.4 cm. The charge on the inner shell is 5.03 × 10⁻⁸ C and that on the outer shell is 2.77 × 10⁻⁸ C. Find the electric field (a) at r = 11.1 cm and (b) at r = 36.1 cm.

a. E(r) = 3.67 x 10⁴ N/C

b. E(r) = 5.38 x 10⁴ N/C

Explanation:

r1 = 8.83 cm

r2 = 15.4 cm

Charge on the inner shell = 5.03 x 10^-⁸ C

Charge on the outer shell = 2.77 x 10^-⁸ C

a)   To find the electric field at r = 11.1 cm,

r₁ = 8.83 cm < r = 11.1 cm < r₂ = 15.4 cm

E(r) = 1               q₁    

          4∈₀        r₂  

E(r) = ( 8.99 x 10⁹ N.m²/C² )  ( 5.03 x 10⁻⁸)

                                 (0.111m)²

E(r) = 3.67 x 10⁴ N/C

b)   To find the electric field at r = 36.1 cm

since r₁  < r₂ < r = 36.1 cm

E(r) = 1               q₁  ₊  q₂  

          4∈₀           r₂  

E(r) = ( 8.99 x 10⁹ N.m²/C² )  ( 5.03 + 2.77 )(1 x 10⁻⁸)

                                             (0.361m)²

E(r) = 5.38 x 10⁴ N/C