Textbook Question
What diameter should the nichrome wire in FIGURE P27.62 be in order for the electric field strength to be the same in both wires?
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27. Resistors & DC Circuits
Intro to Current
Problem 41a
Textbook Question
The electron beam inside an old television picture tube is 0.40 mm in diameter and carries a current of 50 μA. This electron beam impinges on the inside of the picture tube screen. How many electrons strike the screen each second?
Verified step by step guidance1
Understand the problem: The goal is to determine how many electrons strike the screen each second. This involves using the relationship between current, charge, and time.
Recall the formula for current: \( I = \frac{Q}{t} \), where \( I \) is the current, \( Q \) is the total charge, and \( t \) is the time. Rearrange this formula to find \( Q \): \( Q = I \cdot t \).
Determine the charge of a single electron: The elementary charge \( e \) is \( 1.6 \times 10^{-19} \, \text{C} \). The total number of electrons \( n \) can be found using \( Q = n \cdot e \). Rearrange this to find \( n \): \( n = \frac{Q}{e} \).
Substitute \( Q = I \cdot t \) into \( n = \frac{Q}{e} \): \( n = \frac{I \cdot t}{e} \). Since we are calculating the number of electrons per second, set \( t = 1 \; \text{s} \).
Substitute the given values into the formula: \( I = 50 \; \mu\text{A} = 50 \times 10^{-6} \; \text{A} \) and \( e = 1.6 \times 10^{-19} \; \text{C} \). Use these values to compute \( n \) using \( n = \frac{I \cdot t}{e} \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Current
Current is the flow of electric charge, measured in amperes (A). In this context, the current of 50 μA (microamperes) indicates the rate at which electrons are flowing through the beam. Since 1 ampere equals 1 coulomb per second, this means that 50 μA corresponds to 50 x 10^-6 coulombs per second.
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Intro to Current
Charge of an Electron
The charge of a single electron is approximately -1.6 x 10^-19 coulombs. This fundamental property allows us to calculate the number of electrons based on the total charge flowing per second. By knowing the total current, we can determine how many individual electrons contribute to that current.
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Calculating Number of Electrons
To find the number of electrons striking the screen each second, we can use the formula: number of electrons = total charge per second / charge of one electron. By substituting the current value (in coulombs) and the charge of an electron, we can easily compute the total number of electrons impacting the screen in one second.
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