Simple lab calculation (Magneticfield vectors)

[Xeno24]

Homework Statement

I = 2.89amps, r = 0.035m, resultant vector angle (55), proporptionality constant (2 x 10^-7)

Homework Equations

B = K X I / r , trigonometry, vector divisions.

The Attempt at a Solution

Hi, I'm just pasting this off my lab to make sure I've done it correctly. Thanks in advance.

Lab:

A rod is put, parallel to the Earth's magnetic field (due north)with a compass needle 0.035m below it. A flow of 2.89amps is switched on and the compass needle deviates 55 degrees due east as the current creates a magnetic field of its' own.

Question - Calculate the Earth's magnetic field density (B) using these vectors.

Using the formula above the field density for the X component is

(2 x 10^-7) x 2.89amp
------------------------------ = 1.651428571 x 10 ^- 5 Tesla
0.035m

To find the resultant vector (B-res), I used

Cos(35) = B-x/B-res, B-x/Cos(35) = B-res,

1.651428571 x 10 ^- 5 T

----------------------------------- = B-res
Cos(35)

B-res = 2,016022035 x 10^-5 T

And finally with Pythagoras you can find the vector of the Y-component,
______________
\/B-res^2 – B-x^2 = 1,156342737 x 10^-5 T

~ 12microT
Since the compass stays in the resultant vector (Bres),

 

[Redbelly98]

Looks good. You could also use the fact that

tan(35 deg) = ____ / ____ ?

which gets you from Bwire to Bearth in a single step, without the need to calculate Bres.

p.s. welcome to PF

 

[Xeno24]

Thanks. :)