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Chapter 17: Problem 66

Before a lightning strike can occur, the breakdown limit for damp air must be reached. If this occurs for an electric field of $3.33 \times 10^{5} \mathrm{V} / \mathrm{m},$ what is the maximum possible height above the Earth for the bottom of a thundercloud, which is at a potential $1.00 \times 10^{8} \mathrm{V}$ below Earth's surface potential, if there is to be a lightning strike?

Short Answer

Expert verified
Answer: Approximately \(300.3 \mathrm{m}\).

Step by step solution

01

Understand the relation between electric field, voltage difference, and distance

An electric field (E) can create a potential difference (V) which is the product of the electric field and the distance (d) between the points. Mathematically, it is given by: \(V = E \times d\) where V is the potential difference, E is the electric field strength, and d is the distance between the points
02

Use given values for electric field and voltage difference

The electric field strength at which the breakdown limit of damp air is reached (E) is given as \(3.33 \times 10^{5} \mathrm{V/m}\). The potential difference between the bottom of the thundercloud and Earth's surface is given as \(1.00 \times 10^{8} \mathrm{V}\).
03

Rearrange the equation to find distance (d)

To find the maximum possible height (d) at which a thundercloud can exist, we can rearrange the equation from step 1 to solve for d, given as: \(d = \frac{V}{E}\) Substitute the values of V and E into the equation: \(d = \frac{1.00 \times 10^{8} \mathrm{V}}{3.33 \times 10^{5} \mathrm{V/m}}\)
04

Calculate the maximum height (d)

Divide the given numbers to find the maximum height: \(d = \frac{1.00 \times 10^{8}}{3.33 \times 10^{5}}\) \(d = 300.3 \mathrm{m}\) So, the maximum possible height above the Earth for the bottom of a thundercloud, which is at a potential \(1.00 \times 10^{8} \mathrm{V}\) below Earth's surface potential, to have a lightning strike is approximately \(300.3 \mathrm{m}\).

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Most popular questions from this chapter

A spherical conductor with a radius of \(75.0 \mathrm{cm}\) has an electric field of magnitude \(8.40 \times 10^{5} \mathrm{V} / \mathrm{m}\) just outside its surface. What is the electric potential just outside the surface, assuming the potential is zero far away from the conductor?
In capacitive electrostimulation, electrodes are placed on opposite sides of a limb. A potential difference is applied to the electrodes, which is believed to be beneficial in treating bone defects and breaks. If the capacitance is measured to be \(0.59 \mathrm{pF},\) the electrodes are \(4.0 \mathrm{cm}^{2}\) in area, and the limb is \(3.0 \mathrm{cm}\) in diameter, what is the (average) dielectric constant of the tissue in the limb?
(a) If the bottom of a thundercloud has a potential of $-1.00 \times 10^{9} \mathrm{V}\( with respect to Earth and a charge of \)-20.0 \mathrm{C}$ is discharged from the cloud to Earth during a lightning strike, how much electric potential energy is released? (Assume that the system acts like a capacitoras charge flows, the potential difference decreases to zero.) (b) If a tree is struck by the lightning bolt and \(10.0 \%\) of the energy released vaporizes sap in the tree, about how much sap is vaporized? (Assume the sap to have the same latent heat as water.) (c) If \(10.0 \%\) of the energy released from the lightning strike could be stored and used by a homeowner who uses \(400.0 \mathrm{kW}\). hr of electricity per month, for how long could the lightning bolt supply electricity to the home?
A defibrillator consists of a 15 - \(\mu\) F capacitor that is charged to $9.0 \mathrm{kV} .\( (a) If the capacitor is discharged in \)2.0 \mathrm{ms}$, how much charge passes through the body tissues? (b) What is the average power delivered to the tissues?
A positively charged oil drop is injected into a region of uniform electric field between two oppositely charged, horizontally oriented plates spaced $16 \mathrm{cm}$ apart. If the mass of the drop is \(1.0 \times 10^{-13} \mathrm{kg}\) and it remains stationary when the potential difference between the plates is $9.76 \mathrm{kV},$ what is the magnitude of the charge on the drop? (Ignore the small buoyant force on the drop.)
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