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In an ionic solution, \(5.0 \times 10^{15}\) positive ions with charge \(+2 e\) pass to the right each second while \(6.0 \times 10^{15}\) negative ions with charge \(-e\) pass to the left. What is the current in the solution?

Short Answer

Expert verified
The current in the solution is \(\frac{Q_{net}}{1}\) A.

Step by step solution

01

Calculate Total Positive Charge

First, calculate the total positive charge. A single ion has charge \(+2e\), and there are \(5.0 \times 10^{15}\) such ions passing to the right each second. So the total positive charge \(Q_{positive}\) is \( 5.0 \times 10^{15} \times 2 \times 1.6 \times 10^{-19}\) C.
02

Calculate Total Negative Charge

Next, calculate the total negative charge. A single ion has charge \(-e\), and there are \(6.0 \times 10^{15}\) such ions passing to the left each second. So the total negative charge \(Q_{negative}\) is \(6.0 \times 10^{15} \times (-1) \times 1.6 \times 10^{-19}\) C.
03

Calculate Net Charge

Now, calculate the net charge. Since the ions are moving in opposite directions, their charges will add up (with the negative charge subtracting from the positive one). So, the net charge \(Q_{net}\) is \(Q_{positive} + Q_{negative}\).
04

Calculate Current

Lastly, use the formula \(I = \frac{Q}{t}\) to calculate the current. Here, \(Q\) is the net charge (which you've calculated in Step 3), and \(t\) is the time, which is 1 second in this context. So, the current \(I\) is \(\frac{Q_{net}}{1}\).

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Key Concepts

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

Electric Charge
Electric charge is a fundamental property of particles that defines their electromagnetic interaction. Typically measured in coulombs (C), charge is possessed by subatomic particles; electrons carry a negative charge, while protons carry a positive one. Charges can be transferred between objects or through materials, often creating an electric current.

In any given system, the total charge is the sum of the individual charges. In the exercise, we detect the presence of ions, which are atoms or molecules with a net electric charge due to the loss or gain of one or more electrons. Calculating the net charge involves considering both the quantity of ions and the magnitude of charge each ion carries. The solution method provided involves this calculation, which is essential in determining the ionic current.
Current Calculation in Physics
When it comes to understanding electric current, it is defined as the flow of electric charge through a given point or region. To calculate this current, one commonly used formula is \(I = \frac{Q}{t}\), where \(I\) represents the current, \(Q\) is the total charge flowing, and \(t\) is the time it takes for this charge to flow. The standard unit of current is the ampere (A).

To break down the steps from the exercise: First we find the total charge by multiplying the number of ions passing a point by their individual charge, then this total charge is divided by the time interval, which results in the current. This straightforward method simplifies the concept of current calculation, enabling students to easily apply it to diverse physics problems involving electric charge movement.
Movement of Ions
In the field of electrochemistry and physics, the movement of ions is central to generating an ionic current. Ions move due to electrical attraction or repulsion, and this movement facilitates the transfer of charge through a medium like an ionic solution. In the exercise, positive ions are moving to the right while negative ions move to the left, demonstrating that ions can flow in different directions, which is essential in the creation of an electric current.

Understanding the direction and magnitude of ion movement is crucial because it affects the net charge flow and therefore the current. The textbook's step-by-step solution exemplifies calculations accounting for the motion and charges of both positive and negative ions. In real-world applications, this concept is foundational in technologies like batteries, where ionic movement is harnessed to store and transfer energy.

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Most popular questions from this chapter

The electron beam inside a television picture tube is \(0.40 \mathrm{mm}\) in diameter and carries a current of \(50 \mu\) A. This electron beam impinges on the inside of the picture tube screen. a. How many electrons strike the screen each second? b. What is the current density in the electron beam? c. The electrons move with a velocity of \(4.0 \times 10^{7} \mathrm{m} / \mathrm{s}\). What electric field strength is needed to accelerate electrons from rest to this velocity in a distance of \(5.0 \mathrm{mm} ?\) d. Each electron transfers its kinetic energy to the picture tube screen upon impact. What is the power delivered to the screen by the electron beam?

A \(2.0 \times 10^{-3}\) V/m electric field creates a \(3.5 \times 10^{17}\) electrons/s current in a 1.0 -mm-diameter aluminum wire. What are (a) the drift speed and (b) the mean time between collisions for electrons in this wire?

A metal wire connecting the terminals of a battery with potential difference \(\Delta V_{\mathrm{bat}}\) gets warm as it draws a current \(I\). a. What is \(\Delta U,\) the change in potential energy of charge \(Q\) as it passes through the wire? b. Where does this energy go? c. Power is the rate of transfer of energy. Based on your answer to part \(a,\) find an expression for the power supplied by the battery to warm the wire. d. What power does a \(1.5 \mathrm{V}\) battery supply to a wire drawing a 1.2 A current?

What fraction of the current in a wire of radius \(R\) flows in the part of the wire with radius \(r \leq \frac{1}{2} R ?\)

A car battery is rated at 90 A hr, meaning that it can supply a 90 A current for 1 hr before being completely discharged. If you leave your headlights on until the battery is completely dead, how much charge leaves the battery?

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