Calculating Current and Magnetic Field of Wire: Magnetism Question Solution

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A compass needle's deflection indicates the influence of a magnetic field created by a current-carrying wire. The problem involves calculating the current's magnitude and direction based on the compass readings in relation to the Earth's magnetic field. The user successfully determined the horizontal and vertical components of the Earth's magnetic field but is struggling to find the wire's magnetic field components. Clarification is sought on the appearance of magnetic field lines around a wire, suggesting a gap in the educational material regarding this specific scenario. Understanding the magnetic field lines is crucial for solving the problem effectively.
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Homework Statement



A compas needle points 20 degrees East of North outdoors. However, when it is placed 8cm to the east of a vertical wire inside a building, it points 55 degrees east of north. what is the magnitude and the direction of the current in the wire? the Earth's field is 5.0E-5 and is horizontal

Homework Equations



Sin=O/H Cos=A/H

B=UI/ 2(pi)R

The Attempt at a Solution



i solved for the horizontal and vertical components of the Earth's magnetic field and found the components for the x and y to be 4.56E-5 and 2.04E-5 respectively.

i am stuck on how to find the components for the magnetic field of the wire.

any help will be greatly appreciated
 
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What do the magnetic field lines around a wire look like?
 
there is no diagram, that is all the information given about the problem. i copied the problem word for word out of the book.
 
You didn't cover magnetic field lines in class? The book doesn't cover them in the section preceding the problem?
 
it does, but it doesn't cover this type of question.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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