# Time Dependent Current in a Wire

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In summary, we have an infinite straight wire with a current that varies with time, reaching a maximum value of 5.2 A at 15 seconds and decreasing linearly to -5.2 A at 26 seconds. At a distance of 57 cm from the wire is a conducting loop with sides measuring 27 cm and 50 cm. The question asks for the magnitude of the magnetic flux through the loop at 15 seconds, which can be calculated using the equation B = μ*I/(2*pi*d) and the integral Φ = ∫B*dA. After initial difficulties, the correct solution was found by integrating the flux equation and taking into account the area of the loop.
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## Homework Statement

An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 5.2 A at t = t1 = 15 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -5.2 A at t = t4 = 26 s, passing through zero at t = t3 = 23 s. A conducting loop with sides W = 27 cm and L = 50 cm is fixed in the x-y plane at a distance d = 57 cm from the wire as shown.What is the magnitude of the magnetic flux Φ through the loop at time t = t1 = 15 s?

B = μ*I/(2*pi*d)

I = 5.2 A

Φ = ∫B*dA

## The Attempt at a Solution

I know I need to use the magnetic flux equation in this somehow. I tried integrating the flux equation above to get something like Φ = ∫B*dA = B*A = ((μ*I)/(2*pi*(((d+L)^2) - (d^2)) * (W*L). (?)

However, when I plugged in the values and typed in what I got into the computer, it didn't like what I had. I tried doing everything I could, & I feel like this is a relatively simple problem. What am I doing wrong?

#### Attachments

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Ignore. I just forgot the integral of 1/x. (ln x)

## 1. What is time-dependent current in a wire?

Time-dependent current in a wire refers to the flow of electric charge through a wire over a period of time. It is typically measured in units of amperes (A) and represents the rate at which charge is moving through the wire.

## 2. How does time affect the current in a wire?

Time can affect the current in a wire in several ways. For example, if the wire is connected to a changing voltage source, the current will also change over time. Additionally, the resistance of the wire may also change over time, which can affect the current flowing through it.

## 3. What causes time-dependent current in a wire?

Time-dependent current in a wire can be caused by a variety of factors, such as changing voltage sources, varying resistance, or the presence of magnetic fields. It can also be affected by the properties of the wire itself, such as its length, thickness, and material.

## 4. How is time-dependent current measured?

Time-dependent current can be measured using a device called an ammeter, which is connected in series with the wire. The ammeter measures the flow of charge through the wire and displays it in units of amperes. Other methods of measuring current include using a multimeter or an oscilloscope.

## 5. What are some real-world applications of time-dependent current in a wire?

Time-dependent current in a wire has many practical applications, such as powering electronic devices, transmitting electricity over long distances, and controlling the speed and direction of electric motors. It is also essential in many scientific and engineering fields, including telecommunications, power generation, and circuit design.

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