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During a particular thunderstorm, the electric potential difference between a cloud and the ground is \(V_{\text {cloud }}-V_{\text {ground }}=1.3 \times 10^{8} \mathrm{V},\) with the cloud being at the higher potential. What is the change in an electron's electric potential energy when the electron moves from the ground to the cloud?

Short Answer

Expert verified
The change in the electron's electric potential energy is \(-2.08 \times 10^{-11} \text{ J}\).

Step by step solution

01

Understanding the Problem

We need to find the change in electric potential energy for an electron moving from the ground to the cloud. The given electric potential difference is \( V = 1.3 \times 10^8 \text{ V} \) and the charge of an electron \( e = -1.6 \times 10^{-19} \text{ C} \).
02

Using the Electric Potential Energy Formula

The formula for electric potential energy change \( \Delta U \) is \( \Delta U = q \times \Delta V \), where \( q \) is the charge of the electron, and \( \Delta V \) is the potential difference.
03

Substituting Known Values

Substitute the values for the charge of an electron \( q = -1.6 \times 10^{-19} \text{ C} \) and the potential difference \( \Delta V = 1.3 \times 10^8 \text{ V} \) into the formula: \( \Delta U = (-1.6 \times 10^{-19} \text{ C}) \times (1.3 \times 10^8 \text{ V}) \).
04

Calculating the Change in Electric Potential Energy

Perform the multiplication: \( \Delta U = -1.6 \times 1.3 \times 10^{-19+8} \). Calculate the product: \( \Delta U = -2.08 \times 10^{-11} \text{ J} \).
05

Interpreting the Result

The negative sign in the result indicates that the electron loses electric potential energy when moving from the ground to the cloud, which is consistent with it moving to a higher potential.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electric Potential Difference
Electric potential difference represents the work needed per unit charge to move a charge between two locations in an electric field. In simpler terms, it is the 'push' that drives charges to move from one point to another, caused by differences in electric potential. The unit of electric potential difference is the volt (V). During a thunderstorm, this potential difference between a cloud and the ground can be extremely high, like the 1.3 x 10^8 volts we have in our example here.
The electric potential difference plays a crucial role in the exchange of electric potential energy. It is the reason electrons move in circuits and during electrical phenomena like lightning.
  • If you have a large potential difference, you'll get a strong force acting on the charges.
  • This force can do work or cause the charges to accelerate.
In our case, the high potential difference is responsible for moving the charge of an electron from the ground up to the cloud.
Electron Charge
The electron charge is a fundamental property of matter, and in simple terms, it defines how an electron interacts within an electric field. Electrons carry a negative charge, which is quantified as approximately \( -1.6 \times 10^{-19} \text{C} \). This charge is what causes electrons to be attracted to positive charges and repelled by negative charges.
Understanding electron charge helps explain why energy calculations, like those we performed earlier, result in negative values when considering electron movement:
  • A negative charge moving toward a higher potential results in a loss of electric potential energy.
  • This loss is represented by a negative change in potential energy.
The electron's charge is constant and doesn't change. However, the energy associated with this charge can vary depending on the potential difference it experiences as it moves.
Electric Field
An electric field is a region around a charged object where forces are exerted on other charges. You can imagine it like a field of force radiating from a single point. The strength and direction of an electric field can be described mathematically, and its presence affects charges placed within it.
The electric field between the cloud and the ground during a thunderstorm is significant. It results from the large electric potential difference and affects how electrons travel from one location to another:
  • An electric field points in the direction that a positive charge would move.
  • For negative charges, like electrons, they will move in the opposite direction to the field lines.
The electric field directly influences the motion of charges. A stronger field results in greater forces, causing charges to move more energetically. During a thunderstorm, this field helps guide the electrons from the cloud to the ground or vice versa, depending on the situation.

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Most popular questions from this chapter

Four identical charges \((+2.0 \mu \mathrm{C}\) each \()\) are brought from infinity and fixed to a straight line. The charges are located \(0.40 \mathrm{m}\) apart. Determine the electric potential energy of this group.

A charge of \(+125 \mu C\) is fixed at the center of a square that is \(0.64 \mathrm{m}\) on a side. How much work is done by the electric force as a charge of \(+7.0 \mu \mathrm{C}\) is moved from one corner of the square to any other empty corner? Explain.

A charge of \(-3.00 \mu \mathrm{C}\) is fixed in place. From a horizontal distance of \(0.0450 \mathrm{m},\) a particle of \(\operatorname{mass} 7.20 \times 10^{-3} \mathrm{kg}\) and charge \(-8.00 \mu \mathrm{C}\) is fired with an initial speed of \(65.0 \mathrm{m} / \mathrm{s}\) directly toward the fixed charge. How far does the particle travel before its speed is zero?

A particle is uncharged and is thrown vertically upward from ground level with a speed of \(25.0 \mathrm{m} / \mathrm{s}\). As a result, it attains a maximum height \(h\). The particle is then given a positive charge \(+q\) and reaches the same maximum height \(h\) when thrown vertically upward with a speed of \(30.0 \mathrm{m} / \mathrm{s}\). The electric potential at the height \(h\) exceeds the electric potential at ground level. Finally, the particle is given a negative charge \(-q .\) Ignoring air resistance, determine the speed with which the negatively charged particle must be thrown vertically upward, so that it attains exactly the maximum height h. In all three situations, be sure to include the effect of gravity.

If the electric field inside a capacitor exceeds the dielectric strength of the dielectric between its plates, the dielectric will break down, discharging and ruining the capacitor. Thus, the dielectric strength is the maximum magnitude that the electric field can have without breakdown occurring. The dielectric strength of air is \(3.0 \times 10^{6} \mathrm{V} / \mathrm{m},\) and that of neoprene rubber is \(1.2 \times 10^{7} \mathrm{V} / \mathrm{m} .\) A certain air-gap, parallel plate capacitor can store no more than 0.075 J of electrical energy before breaking down. How much energy can this capacitor store without breaking down after the gap between its plates is filled with neoprene rubber?

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