Determining a value for the magnetic force constant (k) (1 Viewer)

[john_citizen]

At school this is the basis of our Practical Test, how would you go about determining a value for the magnetic force constant (k)

Aim: To make measurements of the deflection of a compass needle caused by nearby current carrying wire, to allow a rough estimate of the strength of the Earth's magnetic field.

Theory: A magnetic compass needle aligns itself with the Earth's magnetic field. When a current carrying wire is placed, parallel to, and directly above the compass, the magnetic field interacts with the Earth's magnetic field to create a resultant field, the direction of which is shown by the direction of the compass needle.

When the switch in the circuit is closed the potential difference established causes a current flow through the straight length of wire. The magnetic field produced by the current carrying wire is perpendicular to the Earth's field and the two fields interact to create a resultant magnetic field with the direction of this field indicated by the compass needle. With appropriate theoretical considerations, measurement of the deflection of the needle for different currents can allow analysis to enale a calculatioin of the strength of the Earths magnetic field.

The experiment is based on the following dot point from the Physics stage 6 syllabus:

Discuss the effect on the magnitude of the force on a current carrying conductor of variations in the magnitude of the current in the conductor

Please Help, on how you would determine k;

Hints - I think it has something to do with equating two equations (F = B I l sin(theta)) and (B = k I / d)

 

[pdang]

From what I read, I don't think you need to experimentally determine the value of k. I would just take the value 2*10^-7 Tm/A.
Also, the equation F=BIl sin(theta) is not relevant here since it applies to the force on a moving charge.

What you can do to get B_earth is graph tan(theta) against B_wire, where theta is the angle of deflection, since tan(theta) = B_wire/B_earth.
Find the gradient of your line and get the reciprocal to get B_earth.

 

[john_citizen]

thank you, your answer was really helpful