## College Physics (4th Edition)

$\lambda = -3.72\times 10^{-23}~C/m$
Since the electron is suspended, the electric force exerted on the electron is equal in magnitude to the electron's weight. We can find the magnitude of the linear charge density: $E~\vert q \vert = mg$ $(\frac{\lambda}{2\pi~\epsilon_0~r})~(\vert q \vert) = mg$ $\lambda = \frac{2\pi~\epsilon_0~r~mg}{\vert q \vert}$ $\lambda = \frac{(2\pi)~(8.854\times 10^{-12}~F/m)~(0.012~m)~(9.109\times 10^{-31}~kg)(9.80~m/s^2)}{1.6\times 10^{-19}~C}$ $\lambda = 3.72\times 10^{-23}~C/m$ Since the electric force exerted on the electron is directed upward, the linear charge density must have a negative value. Therefore, $\lambda = -3.72\times 10^{-23}~C/m$