# Find the magnetic field at a point

## Homework Statement 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 ?

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BvU
Homework Helper
2019 Award
Know about the right-hand rule ?

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

BvU
Homework Helper
2019 Award
Yeah
So draw the arrows to find how you have to add them.

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 , Bnet = √(82+62) = 10 μT ?

BvU
Homework Helper
2019 Award
the direction of I2 is (-i)
I'd vote for $-\hat k$ I'd vote for $-\hat k$ So , B2 ($-\hat j$)
B1 ($\hat i$)

BvU
Homework Helper
2019 Award
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: $\ \hat\imath,\ \hat\jmath$

• Fatima Hasan