Magnetic Fields and wires question

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Homework Statement

Calculate the magnitude of the magnetic field at a point midway between two long, parallel wires that are 1.0m apart and have currents if 10A and 20A, respectively, if the currents are a) in opposite directions, and b) in the same direction.

Homework Equations

µ = 4*pi*10^-7

B = µ(I/2*pi*r)

The Attempt at a Solution

:(

 

[rss14]

I figured out HOW to do it, just not WHY.

r = 0.5m (because the point is between the wires)

For
a) You add the currents, so the current will be 20A + 10A = 30A. This will give the correct magnetic field, B = 1.2E-5 T.

b) You subtract the current, so the current is 20A - 10A = 10A. This will give the correct magnetic field, B = 4.0E-6 T.

Why does it work this way?

 

[rss14]

This this have anything to do with it:

When the currents are in the same direction, the magnetic fields oppose each other.

When the currents are in the opposite direction, the magnetic fields add onto each other?

(Use the right hand rule to picture this)

?

 

[Ouabache]

Yes you have answered your own question. The fields do combine as you have deduced and can be pictured (as you have noted), using the right hand rule.