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## Homework Statement

In a laboratory we want to measure the value Bt which is Earth's magnetic field.

We got a magnetic needle which is held by a wire, when the needle points out Earth's magnetic field, it creates a 64.5 degree angle in comparison to the horizontal Bh which is the table. The axis of the needle is Earth's magnetic field called Bt, it can be divided in Bv, the vertical line which is perpendicular to the horizontal and Bh which is the horizontal.

First we want to know the horizontal Bh so we put the needle in a solenoid, the needle is perpendicular to the magnetic field line Bs of the solenoid when there's no current, then we turn on the solenoid which creates a 5,0*10^-4 Tesla field called Bs, the needle rotates by 68 degrees.

Questions : We want the value of Bh which is the horizontal and Bt which is the Earth's magnetic field at Paris. ( the value is made at Paris)

## Homework Equations

With trigonometry calculus I found Bh = Bs/tan(68) = 5.0*10^-4/tan(68) = 2.0*10^-4 T

## The Attempt at a Solution

Here's the problem, when I look for Bt I got those calculus : Bt = Bh/cos(64.5) = 2.0*10^-4/cos(64.5) = 4.7*10^-4 T

I checked up on the web for Earth's magnetic field in Paris, it's 47 microtesla but the micro order of magnitude is 10^-6 so my result is 470 microtesla, ten times greater than what should be expected!

Which mistake did I do?

Thanks.