Chapter 25: Q30P (page 742)

How much energy is stored in $1.00 m^{3}$ of air due to the “fair weather” electric field of magnitude 150 V/m?

Short Answer

Expert verified

The energy stored in $1.00 m^{3}$ of air due to the “fair weather” electric field of magnitude 150 V/m is $9.96 \times 10^{- 8} J$ .

Step by step solution

The given data

a) Volume of air, $V = 1.00 m^{3}$

b) Magnitude of electric field,E =150 V/m

Understanding the concept of the stored energy

We need to use the equation of the energy density and the energy stored per unit volume in the magnitude E of the electric field. Using the given formulae, we can get the required value of the stored energy.

Formulae:

The energy density of an electric field, $u = \frac{1}{2} ε_{0} E^{2}$ ...(i)

The energy stored per unit volume in the electric field, $u = \frac{U}{V}$ ...(ii)

Step 3: Calculation of the stored energy

Using equations (i) and (ii), we can get the energy stored in the electric field as follows: ( $ε_{0} = 8.85 \times 10^{- 12} \frac{C^{2}}{N . m^{2}}$ is permittivity of free space)

$U = \frac{1}{2} ε_{0} E^{2} V = \frac{1}{2} (8.85 \times 10^{- 12} \frac{C^{2}}{N . m^{2}}) {(150 \frac{V}{m})}^{2} (1.00 m^{3}) = 9.96 \times 10^{- 8} J$

Hence, the value of the stored energy is $9.96 \times 10^{- 8} J$ .

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How much energy is stored in $1.00 m^{3}$ of air due to the “fair weather” electric field of magnitude 150 V/m?

Short Answer

Step by step solution

The given data

Understanding the concept of the stored energy

Step 3: Calculation of the stored energy

One App. One Place for Learning.

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How much energy is stored in 1.00m3of air due to the “fair weather” electric field of magnitude 150 V/m?

Short Answer

Step by step solution

The given data

Understanding the concept of the stored energy

Step 3: Calculation of the stored energy

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Famous Physicists

Electricity and Magnetism

Medical Physics

Energy Physics

Mechanics and Materials

Engineering Physics

Study anywhere. Anytime. Across all devices.

How much energy is stored in $1.00 m^{3}$ of air due to the “fair weather” electric field of magnitude 150 V/m?