# Chapter 26 - The Electric Field - Conceptual Questions: 8

The surface charge density will be $2~nC/cm^2$

#### Work Step by Step

We can write an expression for the initial surface charge density: $\sigma_1 = \frac{q}{A_1}$ If the radius of the disk is doubled, then the area of the disk increases by a factor of 4. That is: $A_2 = 4~A_1$ We can find the final surface charge density: $\sigma_2 = \frac{q}{A_2}$ $\sigma_2 = \frac{q}{4~A_1}$ $\sigma_2 = \frac{\sigma_1}{4}$ $\sigma_2 = \frac{8~nC/cm^2}{4}$ $\sigma_2 = 2~nC/cm^2$ The surface charge density will be $2~nC/cm^2$.

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