Find the magnetic field at a point

[Fatima Hasan]

Homework Statement

Homework Equations

B=(μ₀*I)/(2πr)

The Attempt at a Solution

B₂ = (4*4*10^-7)/(2*0.1)
= 8 μT
B₁ = (3*4*10^-7)/(2*0.1)
= 6μT
Could I know how to determine the directions ?

 

[BvU]

Know about the right-hand rule ?

The directions matter (to some extent), but
do the signs matter ? They are only asking for a magnitude ...

 

[Fatima Hasan]

Know about the right-hand rule ?

Yeah

 

[BvU]

Yeah

So draw the arrows to find how you have to add them.

 

[Fatima Hasan]

So draw the arrows to find how you have to add them.

B₂ = 8μT (-j) , because the direction of I₂ is (-i).
B₁ = 6μT (i) , because the direction of I₁ is (j)
So , B_net = √(8²+6²) = 10 μT ?

 

[BvU]

the direction of I2 is (-i)

I'd vote for $-\hat k$

 

[Fatima Hasan]

I'd vote for $-\hat k$

So , B₂ ($-\hat j$)
B₁ ($\hat i$)

 

[BvU]

I agree. (I also agreed with #5, except for the directions of the currents )

I hope you now understand my frivolous 'do the signs matter': in this case just knowing that the field vectors are perpendicular is enough to get 10 $\mu$T as answer. Normally the signs certainly do matter.

To boot a small $\TeX$ tip: Donald Knuth has provided \imath and \jmath so the hat and the dot don't pile up: $\ \hat\imath,\ \hat\jmath$