Point between two wires at which the flux density is zero

[moenste]

Homework Statement

A long wire (X) carrying a current of 30 A is placed parallel to, and 3.0 cm away from, a similar wire (Y) carrying a current of 6.0 A. What is the flux density midway between the wires: (a) when the currents are in the same direction, (b) when they are in opposite directions? (c) When the currents are in the same direction there is a point somewhere between X and Y at which the flux density is zero. How far from X is this point? (μ₀ = 4 π * 10 ^-7 H m^-1.)

Answers: (a) 3.2 * 10^-4 T, (b) 4.8 * 10^-4 T, (c) 2.5 cm

2. The attempt at a solution
(a) B = μ₀ I / 2 π a = [4 π * 10 ^-7 * (30 - 6)] / 2 π * (0.03 / 2) = 3.2 * 10^-4 T. I is (30 - 6) since the currents are in the same direction and 0.03 is divided by two because we need the flux density midway between the wires.

(b) Same formula but 30 + 6, since the currents are in opposite directions = 4.8 * 10^-4 T.

(c) Regarding this part I don't know. I used the abovementioned formula and got: [4 π * 10 ^-7 * (30 - 6)] / 2 π * a = 0 → 7.2 * 10^-6 a^-1 = 0. And that's as far as I got.

 

[The Buttered Cat]

The way you have it written it looks like you expect the point to be equidistant from both wires. Does that make sense to you, knowing the wires have different currents?

 

[moenste]

The way you have it written it looks like you expect the point to be equidistant from both wires. Does that make sense to you, knowing the wires have different currents?

Hm, I think I got it:
μ₀ I_X / 2 π a_X = μ₀ I_Y / 2 π a_Y
μ₀ I_X 2 π a_Y = μ₀ I_Y 2 π a_X
30 a_Y = 6 a_X
5 a_Y = a_X

We know that a_X + a_Y = 0.03 m

Since we need a_X: a_Y = 0.2 a_X → a_X + 0.2 a_X = 0.03 → 1.2 a_X = 0.03 → a_X = 0.025 cm or 2.5 m.

 

[The Buttered Cat]

aX = 0.025 cm or 2.5 m.

Be careful with your units there, but otherwise you are exactly right.

 

[moenste]

Be careful with your units there, but otherwise you are exactly right.

Oh yes, it's the other way around :). 0.025 m and 2.5 cm.