Question

What electric field can just support a water droplet $1.0\times {10}^{-6}m$ in diameter carrying one electron charge?

• A. $3.21\times {10}^{4}V/m$
• B. $2.31\times {10}^{4}V/m$
• C. $1.32\times {10}^{4}V/m$
• D. None of these

Answer 1

Answer: (A)

$3.21\times {10}^{4}V/m$

It is given that,

$radius\left(r\right)=\frac{diameter}{2}=\frac{1.0\times {10}^{-6}}{2}m$

mass (m) = $\rho \times \frac{4}{3}\times \pi \times \left(r^3\right)$

m = $\frac{4}{3}\times 1000\times \frac{22}{7}\times {(0.5\times {10}^{-6})}^3=5.23\times {10}^{-16}$

we know that ,
charge (q) = $1.602\times {10}^{-19}$ coulombs

gravity (g) = $9.8\frac{m}{s^2}$

substitute these values in the following equation and solve

E = $\frac{(5.23\times {10}^{-16})\times 9.8}{1.602\times {10}^{-19}}=3.21\times {10}^4\frac{V}{m}$

So, the answer is option (A).