Magnetic field in 3 dimensions

[Physicslearner500039]

Homework Statement

One long wire lies along an x axis and carries a current of 30A in the positive x direction. A second long wire is perpendicular to the xy plane, passes through the point (0,4.0 m, 0), and carries a current of 40 A in the positive z direction. What is the magnitude of the resulting magnetic field at the point (0,2.0 m, 0)?

Relevant Equations

Magnetic field due to long wire (μ0*i)/(2*π*r)

The problem is as above, My attempt is as below but there is lot of effort in terms of imagining and not very confident,
Required the magnetic field on the y-axis let us say point P.
The magnetic field due to the x-axis wire is out of the paper at P with the values as R=2.0m, i =30A.
B1 = (μ0*i)/(2*π*r) = (4*π*(10^-7)* 30)/(2*π*2) = 3uT,
For the Z axis wire the magnetic field is again into the paper at P with the values as R=2.0m, i = 40A
B2 = (μ0*i)/(2*π*r) = (4*π*(10^-7)* 40)/(2*π*2) = 4uT. The resultant is 1uT. The answer does not seem to match it is 5uT. Please advise.

 

[TSny]

The two fields are not parallel to each other.

 

[rude man]

For the Z axis wire the magnetic field is again into the paper at P

Really?

 

[Physicslearner500039]

Really?

Yes it is coming out of the paper.

 

[jtbell]

For the Z axis wire the magnetic field is again into the paper at P

How did you conclude this?

(I assume the paper is in the xy-plane, i.e. perpendicular to the z-axis at z = 0.)

 

[TSny]

@Physicslearner500039

Do you agree that the diagram shown below depicts the setup?

 

[Physicslearner500039]

Yes

 

[TSny]

Yes

Good. From the diagram, what is the direction of the magnetic field at the red dot due to current $I_2$?

 

[Physicslearner500039]

Yes i think it is in positive X direction. Am i correct?

 

[TSny]

Yes