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Chapter 25: Q30P (page 742)

How much energy is stored in 1.00m3of air due to the 鈥渇air weather鈥� electric field of magnitude 150 V/m?

Short Answer

Expert verified

The energy stored in 1.00m3 of air due to the 鈥渇air weather鈥� electric field of magnitude 150 V/m is 9.96脳10-8J .

Step by step solution

01

The given data

a) Volume of air, V=1.00m3

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

02

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=12蔚0E2 ...(i)

The energy stored per unit volume in the electric field,u=UV ...(ii)

03

Step 3: Calculation of the stored energy

Using equations (i) and (ii), we can get the energy stored in the electric field as follows: (蔚0=8.85脳10-12C2N.m2is permittivity of free space)

U=12蔚0E2V=128.85脳10-12C2N.m2150Vm21.00m3=9.96脳10-8J

Hence, the value of the stored energy is 9.96脳10-8J.

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Most popular questions from this chapter

A certain substance has a dielectric constant of 2.8and a dielectric strength of 18 MV/m. If it is used as the dielectric material in a parallel plate capacitor, what minimum area should the plates of the capacitor have to obtain a capacitance of 7.0脳10-2渭贵and to ensure that the capacitor will be able to withstand a potential difference of 4.0 kV?

A slab of copper of thickness b=2.00mmis thrust into a parallelplatecapacitor of plate area A=2.40cm2and plate separationd=5.00mm , as shown in Fig. 25-57; the slab is exactly halfway between the plates.(a) What is the capacitance after the slab is introduced? (b) If a chargeq=3.40渭Cis maintained on the plates, what is the ratio of the stored energy before to that after the slab is inserted? (c) How much work is done on the slab as it is inserted? (d) Is the slab sucked in or must it be pushed in?

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Each of the uncharged capacitors in Fig. 25-27 has a capacitance of 25.0渭贵. A potential difference of V=4200Vis established when the switch is closed. How many coulombs of charge then pass through meter A?

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