# Find the magnetic induction vector

• LinguaBrous
LinguaBrous
Homework Statement
Two infinitely long parallel conductors located at a distance of 5 cm from each other carry currents of 1 A and 2 A, respectively, in different directions. What is the direction and magnitude of the magnetic induction vector at a point located at a distance of 3 cm from the first conductor?
Relevant Equations
##\mathbf{B} = \frac{\mu_0 \cdot I}{2\pi \cdot r}##
I can find the magnetic induction vector of the first conductor at a given point using the formula (its 6,667*10^-7 Tl) but I don’t understand what needs to be done with the second conductor. I have come across similar problems in which, however, the distance from the second conductor to the point was given. In those problems, the vector was found using the cosine theorem or other geometric laws. Here I cannot figure out how I should understand at what distance the point is from the second conductor. I guess that I should consider several cases and get several answers for this problem but I don’t quite understand what these cases could be (like building a triangle from 3 points and adding 1 degree to the angle or something like that) Thanks everyone for any help in advance.

There is certainly missing information. Maybe it was supposed to say "a point between them".

haruspex said:
There is certainly missing information. Maybe it was supposed to say "a point between them".
This is the exact text of the problem that my professor wrote on the board.

In any case, during the night I only reached the following: there are 4 cases to consider.

The point lies between them.

The point lies to the left of the first conductor.

The point lies at the same distance from the second conductor as from the first (equilateral triangle).

The point lies so that a right triangle is formed.

Maybe there are some other cases that I have not considered, but for which a solution can be found using this data? Or maybe it's not solved like that at all)

LinguaBrous said:
This is the exact text of the problem that my professor wrote on the board.

In any case, during the night I only reached the following: there are 4 cases to consider.

The point lies between them.

The point lies to the left of the first conductor.

The point lies at the same distance from the second conductor as from the first (equilateral triangle).

The point lies so that a right triangle is formed.

Maybe there are some other cases that I have not considered, but for which a solution can be found using this data? Or maybe it's not solved like that at all)
The possibilities form a complete circle around the first conductor.

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