# Two long wires carrying current

• scrubber
In summary, the values of ∫B⋅ds and ∫E⋅ds depend on the given values of current (I1 and I2) and the closed path (S). For i) I1=I2=1A, the value of ∫B⋅ds is 0, while the value of ∫E⋅ds cannot be determined without knowing the value of Φ. For ii) I1=1A and I2=0A, the value of ∫B⋅ds is μ0, and the value of ∫E⋅ds also cannot be determined without knowing the value of Φ. Regardless of whether the currents are constant
scrubber

## Homework Statement

Two long wires carrying current I1 and I2 in opposite directions pass through a closed path S as shown in the picture.
What are the values of ∫B⋅ds and ∫E⋅ds if:
i) I1=I2=1A
ii) I1=1A and I2=0A?

## Homework Equations

Ampere's Law: ∫B⋅ds=μ0I

## The Attempt at a Solution

For i, ∫B⋅ds=μ0(I1-I2)=μ0(0)=0
For ii, ∫B⋅ds=μ0(I1)=μ0(1)=μ0

Is these correct? But I have no idea of finding ∫E⋅ds

What about the righthand side if you knw the currents are constant ?

scrubber said:

## The Attempt at a Solution

But I have no idea of finding ∫E⋅ds
What is Φ for your situation? Hint: it doesn't matter whether the currents are constant or time-varying.

## 1. What is the formula for calculating the magnetic force between two long wires carrying current?

The formula for calculating the magnetic force between two long wires carrying current is F = (μ0 * I1 * I2 * L) / (2 * π * d), where μ0 is the permeability of free space, I1 and I2 are the currents in the wires, L is the length of the wires, and d is the distance between the wires.

## 2. How does the direction of current flow affect the magnetic force between two long wires?

The direction of current flow in the wires determines the direction of the magnetic field they create. If the currents are flowing in the same direction, the wires will attract each other, and if they are flowing in opposite directions, they will repel each other.

## 3. How is the strength of the magnetic force affected by the distance between the two long wires carrying current?

The strength of the magnetic force between two long wires carrying current is inversely proportional to the distance between the wires. This means that as the distance between the wires increases, the magnetic force decreases.

## 4. What is the direction of the magnetic field created by two long wires carrying current?

The direction of the magnetic field created by two long wires carrying current is determined by the right-hand rule. If you point your right thumb in the direction of the current flow in the first wire, your fingers will curl in the direction of the magnetic field. The direction of the magnetic field will be opposite for the second wire.

## 5. How does the magnetic force between two long wires change if the currents are increased or decreased?

The magnetic force between two long wires carrying current is directly proportional to the current in each wire. This means that if the currents are increased, the magnetic force will also increase, and if the currents are decreased, the magnetic force will decrease.

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