# Point where magnetic field cancels between two current carrying wires.

## Homework Statement

Problem statement along with relevant diagram attached with picture below.

## Homework Equations

The Biot-Savart Law for a long current carrying wire.
B = (μ)(I)/2(pi)(d)
Where d is the perpendicular distance between the wire and the point at which the field is being calculated. μ is the permeability of free space.

## The Attempt at a Solution

(a) Point at which field is null:
Net magnetic field = 0.
Thus, the sum of the magnetic fields at a certain point is 0. (One will point into the page and one will point out of the page)
Thus:
Bnet = 0 ⇔ (μ)(I1)/2(pi)(ρ) = (μ)(I1/2)/2(pi)(d - ρ)
Calculate ρ. I think it works out to be 2d/3.
Could someone tell me if this is correct?
Also, for part (b) what adjustment should be made? Assuming I did (a) correctly. Thanks.

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haruspex
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Gold Member
Bnet = 0 ⇔ (μ)(I1)/2(pi)(ρ) = (μ)(I1/2)/2(pi)(d - ρ)
Calculate ρ. I think it works out to be 2d/3.
Sounds right.
What change do you think it makes to the field from I2?

Will both fields be pointing out of the page (in the positive k) in the region of 0-d?

Sorry! I meant into the page. In the negative k.

haruspex
Homework Helper
Gold Member
Sorry! I meant into the page. In the negative k.
Yes, but I meant, what difference does it make to the equation?

(I)(μ)/(2)(pi)(ρ) - (I/2)(μ)/(2)(pi)(d - ρ) = 0

We'll now have:
(I)(μ)/(2)(pi)(ρ) + (I/2)(μ)/(2)(pi)(d - ρ) = 0
I think the answer works out to be ρ = 2d.

haruspex
Homework Helper
Gold Member