Let's solve the problem step by step. Given: - Radius of the spherical conductor, \( r = 12\,\text{cm} = 0.12\,\text{m} \) - Charge on the sphere, \( Q = 1.6 \times 10^{-7}\,\text{C} \) - We have to find the electric field: - (a) Inside the sphere - (b) Just outside the sphere - (c) At a point \( 18\,\text{cm} = 0.18\,\text{m} \) from the center Let's use the formula for the electric field due to a spherical conductor: ### (a) Electric Field Inside the Sphere For a **conductor**, the electric field **inside** is **zero** (because charges reside on the surface and redistribute to cancel internal fields): \[ E_{\text{inside}} = 0 \] --- ### (b) Electric Field Just Outside the Sphere Just outside the surface, the electric field is: \[ E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r^2} \] Where: - \(\varepsilon_0 = 8.854 \times 10^{-12} \text{ C}^2/\text{N}\cdot\text{m}^2\) - \(Q = 1.6 \times 10^{-7}\, \text{C}\) - \(r = 0.12\,\text{m}\) Plug in the values: \[ E = \frac{1}{4\pi \times 8.854 \times 10^{-12}} \frac{1.6 \times 10^{-7}}{(0.12)^2} \] \[ \frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,\text{N}\cdot\text{m}^2/\text{C}^2 \] \[ E = 9 \times 10^9 \times \frac{1.6 \times 10^{-7}}{(0.12)^2} \] Calculate denominator: \[ (0.12)^2 = 0.0144 \] So, \[ E = 9 \times 10^9 \times \frac{1.6 \times 10^{-7}}{0.0144} \] Calculate numerator: \[ 1.6 \times 10^{-7} \div 0.0144 = \frac{1.6}{0.0144} \times 10^{-7} = 111.11 \times 10^{-7} = 1.1111 \times 10^{-5} \] \[ E = 9 \times 10^9 \times 1.1111 \times 10^{-5} \] \[ E = 9.9999 \times 10^{4} \,\text{N/C} \] So, approximately: \[ \boxed{1.0 \times 10^5\,\text{N/C}} \] --- ### (c) Electric Field at 18 cm from the Center Now, \( r = 0.18\,\text{m} \): \[ E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r^2} = 9 \times 10^9 \times \frac{1.6 \times 10^{-7}}{(0.18)^2} \] \[ (0.18)^2 = 0.0324 \] \[ \frac{1.6 \times 10^{-7}}{0.0324} = \frac{1.6}{0.0324} \times 10^{-7} = 49.3827 \times 10^{-7} = 4.9383 \times 10^{-6} \] \[ E = 9 \times 10^9 \times 4.9383 \times 10^{-6} \] \[ E = 44.4447 \times 10^{3} = 4.44 \times 10^{4}\,\text{N/C} \] --- ## **Final Answers** **(a) Inside the sphere:** \[ \boxed{0\,\text{N/C}} \] **(b) Just outside the sphere:** \[ \boxed{1.0 \times 10^5\,\text{N/C}} \] **(c) At a point 18 cm from the center:** \[ \boxed{4.4 \times 10^4\,\text{N/C}} \]