Question

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.

Answer 1

a. E(r) = 3.67 x 10⁴ N/C

b. E(r) = 5.38 x 10⁴ N/C

Step-by-step 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
`\pi`∈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
`\pi`∈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