An infinite plane carries a surface charge density of 3.54 × 10⁻¹¹ C/m². Compute the field it produces, in N/C, using ε0 = 8.854 × 10⁻¹² F/m. Give the answer to one decimal place.

Practice question · Numerical answer

An infinite plane carries a surface charge density of $3.54 \times 10^{-11}$ C/m $^2$ . Compute the field it produces, in N/C, using $\varepsilon_0 = 8.854 \times 10^{-12}$ F/m. Give the answer to one decimal place.

Hints

Apply Gauss’s law to a pillbox straddling the plane, remembering it has TWO faces.
Compute 3.54e-11 / (2 x 8.854e-12).

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2 (answers within ±0.1 count)

Why

$E = \sigma/2\varepsilon_0 = 3.54\times10^{-11}/(2 \times 8.854\times10^{-12}) = 2.0$ N/C. The factor of two comes from the pillbox having a face on each side of the plane, forgetting it doubles the answer.

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An infinite plane carries a surface charge density of 3.54×10−113.54 \times 10^{-11}3.54×10−11 C/m2^22. Compute the field it produces, in N/C, using ε0=8.854×10−12\varepsilon_0 = 8.854 \times 10^{-12}ε0​=8.854×10−12 F/m. Give the answer to one decimal place.

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An infinite plane carries a surface charge density of $3.54 \times 10^{-11}$ C/m $^2$ . Compute the field it produces, in N/C, using $\varepsilon_0 = 8.854 \times 10^{-12}$ F/m. Give the answer to one decimal place.