A gold foil with surface density 160 mg/ cm² kept on a charged, conducting surface just rises as its weight is balanced by the electric force. Calculate the surface charged density on the conducting surface

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0.6×10^-5 c/m²

1.28×10^-5 c/m²

1.666×10^-5 c/m²

0.52×10^-5 c/m²

answer is A.

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Detailed Solution

$\begin{array}{l} \frac{σ}{2 ε_{0}} q = mg \Rightarrow \frac{σ^{2}}{2 ε_{0}} = \frac{mg}{A} \\ \frac{σ^{2}}{2 \times 8 .85 \times 10^{- 12}} = \frac{160 \times 10^{- 6} \times 10}{10^{- 4}} \\ σ = 1 .666 \times 10^{- 5} C / m^{2} \end{array}$

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