Question

A spherical conductor of radius $10\text{cm}$ has a charge of $3.2\times {10}^{-7}\text{C}$ distributed uniformly. What is the magnitude of electric field at a point $5\text{cm}$ from the surface of the sphere?

• A. $1.28\times {10}^4{\text{NC}}^{-1}$
• B. $1.28\times {10}^5{\text{NC}}^{-1}$
• C. $1.28\times {10}^6{\text{NC}}^{-1}$
• D. $1.28\times {10}^7{\text{NC}}^{-1}$

Answer 1

The correct option is B $1.28\times {10}^5{\text{NC}}^{-1}$



Given, $q=3.2\times {10}^{-7}\text{C}d=r+5=10+5=15\text{cm}$


Field at any point outside the spherical shell is,

$E=\frac{1}{4\pi {\epsilon }_0}\frac{q}{d^2}$

$=\frac{9\times {10}^9\times 3.2\times {10}^{-7}}{(15\times {10}^{-2}{)}^2}=\frac{9\times 3.2\times {10}^6}{225}$

$=\frac{288}{225}\times {10}^5$

$=1.28\times {10}^5{\text{NC}}^{-1}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (b) is the correct answer.