# Time Dependent Current in a Wire

• Flop880
In summary, the conversation involves a problem with finding the magnetic flux through an area, using the formula B=uI/2(pi)(d) and integrating over the area to find the total flux. The person initially made a mistake in their calculation, but later corrected it and got the right answer. The concept of double integrals is also briefly mentioned.
Flop880

## Homework Statement

Problem is attached

## Homework Equations

A formula sheet is also attached

## The Attempt at a Solution

flux=$\int$B dA from .31m to .82
B=u I(enclosed)/2(pi)(d)
d=x
dA=dx L
so ∫ (u)(I)(L)dx / 2(pi)(x) from .31m to .82m remember x=d in the pic. My answer is 3.9687e-7 and its wrong

integral came out to be (u)(I)(L)/2pi (ln(.82) - ln(.31))
u=4(pi)e-7
I=4A

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Flop880 said:

## Homework Statement

Problem is attached

## Homework Equations

A formula sheet is also attached

## The Attempt at a Solution

flux=$\int$B dA from .31m to .82
That "dA" indicates an area - so why is this not a double integral?

B=u I(enclosed)/2(pi)(d)
d=x
dA=dx L
so ∫ (u)(I)(L)dx / 2(pi)(x) from .31m to .82m remember x=d in the pic. My answer is 3.9687e-7 and its wrong
I don't think you've used the formula correctly or you got confused between two different uses.
$$B=\frac{\mu_0 I}{2\pi d}$$... would be the magnetic field strength a distance d from a long straight wire.

The magnetic flux through area dA at position (x,y) would be ##d\Phi = B(x,y,t)\;dA##
You'd have to integrate over the whole LxW area to find the total flux.

I just got the right answer by multiplying by the width, not length. so dA= dx w, since dx is the length that's changing times the width which gives area. What do you mean by double integral? Doesn't that give volume?

Well done.

note:
Triple integrals give volume. dV=dx.dy.dz,

dA=W.dx is only true when the thing you are integrating does not vary with y
- which is what you have.

Last edited:

L=1mThe time dependent current in a wire can be calculated using the formula B=uI(enclosed)/2(pi)(d), where B is the magnetic field, u is the permeability of the material, I is the current, and d is the distance from the wire. In this case, the current is time dependent, which means that it is changing over time. To calculate the total magnetic flux, we need to integrate the formula over the entire length of the wire.

The integral of B=uI(enclosed)/2(pi)(d) over the length of the wire can be written as ∫ (u)(I)(L)dx / 2(pi)(x) from .31m to .82m, where u is the permeability, I is the current, L is the length of the wire, and dx is the infinitesimal distance along the wire. Remember that x is equal to d in the picture.

Substituting the given values of u=4(pi)e-7, I=4A, and L=1m, we get ∫ (4(pi)e-7)(4A)(1m)dx / 2(pi)(x) from .31m to .82m. Evaluating this integral, we get (4(pi)e-7)(4A)(1m)/2(pi) (ln(.82) - ln(.31)). Plugging in the values, we get a final answer of 3.9687e-7.

It is important to note that the units of the final answer are Tesla-meters squared (Tm^2), which is the unit of magnetic flux. Also, make sure to double check the units of all the given values to ensure consistency in the final answer.

## What is time dependent current in a wire?

Time dependent current in a wire refers to the change in the flow of electric current over time. This can occur due to various factors such as changes in voltage, resistance, and external magnetic fields.

## How is time dependent current different from steady-state current?

Steady-state current refers to a constant flow of electric current in a wire, whereas time dependent current involves changes in the current over time. Steady-state current is often used in simple circuits, while time dependent current is more commonly observed in complex systems.

## What causes time dependent current in a wire?

Time dependent current can be caused by a variety of factors, such as changes in the external magnetic field, changes in the voltage or resistance of the wire, or the presence of varying components in the circuit.

## How is time dependent current measured?

Time dependent current can be measured using a variety of instruments, such as an ammeter or oscilloscope. These devices can track changes in the current over time and provide a visual representation of the current's behavior.

## What are the practical applications of studying time dependent current in a wire?

Studying time dependent current in a wire is important in various fields, such as electrical engineering and physics. It can help in understanding the behavior of complex circuits and designing more efficient systems. It also has practical applications in fields such as telecommunications, power generation, and electronic devices.

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