Loop, compass and magnetic field

[Mantaray]

Homework Statement

A compass is placed in the middle of a metal loop with radius 0.10m. The compass points in the direction of the Earth magnetic field when the loop is at rest. When the loop revolves around an axis perpendicular to the Earth's surface with constant angular velocity, the average deviation of the compass needle is 2 degrees. Find the resistance R of the metal loop.

Homework Equations

Relevant Equations and attempt at solution are both in the .pdf file.

The Attempt at a Solution

 

[berkeman]

Homework Statement

A compass is placed in the middle of a metal loop with radius 0.10m. The compass points in the direction of the Earth magnetic field when the loop is at rest. When the loop revolves around an axis perpendicular to the Earth's surface with constant angular velocity, the average deviation of the compass needle is 2 degrees. Find the resistance R of the metal loop.

Homework Equations

Relevant Equations and attempt at solution are both in the .pdf file.

The Attempt at a Solution

You are on the right track. Here's a link to help you calculate the B-field at the center of the loop of current:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html

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[Mantaray]

Thank you!
Knowing that the magnetic field strength induced by the loop equals, I could decompose that vector into one which is parallel to the Earth magnetic field by multiplying with sin(omega t) and one which is perpendicular to the Earth magnetic field by multiplying with cos(omega t).
I think I'm able to work out the answer from here on.

However, is there an additional way to solve this problem without applying the Biot-Savart law, or is it mandatory to first deduce the Biot-Savart law from Ampère's law?