A region has a uniform electric field of 2.0 × 10³ V/m. Compute the electrostatic energy density in units of 10⁻⁵ J/m³, using ε0 = 8.854 × 10⁻¹² F/m. Give the answer to one decimal place.

Physics II / Electrostatic Energy and Forces

Practice question · Numerical answer

A region has a uniform electric field of $2.0 \times 10^3$ V/m. Compute the electrostatic energy density in units of $10^{-5}$ J/m $^3$ , using $\varepsilon_0 = 8.854 \times 10^{-12}$ F/m. Give the answer to one decimal place.

Hints

Energy density is one half epsilon-zero times the field squared.
Compute 0.5 x 8.854e-12 x (2.0e3)^2.

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1.8 (answers within ±0.1 count)

Why

$u = \tfrac{1}{2}\varepsilon_0 E^2 = 0.5 \times 8.854 \times 10^{-12} \times 4.0 \times 10^6 = 1.77 \times 10^{-5}$ J/m $^3$ . Even a fairly strong laboratory field stores very little energy per cubic metre.

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A region has a uniform electric field of 2.0×1032.0 \times 10^32.0×103 V/m. Compute the electrostatic energy density in units of 10−510^{-5}10−5 J/m3^33, 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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More questions on Electrostatic Energy and Forces

A region has a uniform electric field of $2.0 \times 10^3$ V/m. Compute the electrostatic energy density in units of $10^{-5}$ J/m $^3$ , using $\varepsilon_0 = 8.854 \times 10^{-12}$ F/m. Give the answer to one decimal place.