Calculate the value of magnetic flux density in air

[flyingpig]

Homework Statement

Calculate the value of magnetic flux density in air in the middle of two straight parallel wires carrying currents of 10A and 20A in the opposite directions. The distance between wires is 10cm.

The Attempt at a Solution

$$\oint \vec{B}\cdot d\vec{A} = \Phi$$
$$\oint \frac{\mu_0 I}{2\pi r}\cdot d\vec{A} = \Phi$$

$$\sum \vec{B} = \frac{\mu_0 (10)}{2\pi r} + \frac{\mu_0 (20)}{2\pi r} = \frac{\mu_0 (30)}{2\pi r}$$

$$30\int \frac{\mu_0 }{2\pi r}\cdot d\vec{A} = \Phi$$

Problem is that I don't know how to transform this into a definite integral. I don't know how long the wires are to do dA to dxdy

 

[SammyS]

It's not asking for the magnetic flux, Φ, it's asking for the 'Magnetic flux density', which is the B field.

I suppose 'in the middle' means halfway between.

 

[flyingpig]

magnetic flux density is magnetic field?

 

[flyingpig]

why would they use such an unnecessary word?

 

[gneill]

why would they use such an unnecessary word?

So that you will learn what is the connection between flux and magnetic field strength

 

[flyingpig]

But what is magnetic flux density really mean? lie flux per volume or something?

 

[gneill]

But what is magnetic flux density really mean? lie flux per volume or something?

The interpretation in terms of lines of flux would be the number of flux lines per unit cross sectional area. You might want to think of it in terms of Gauss' Law, where you look at the flux through a surface area.

A unit of magnetic flux is the weber (wb). A unit of magnetic field strength is the Tesla. One Tesla = one wb/m².