Will a magnetic field in a permanent magnet become not-uniform and cause magnetic force to be different throughout the experiment, and, if so, what are the causes of it and how do I prevent this?
I'm doing an experiment to investigate the effects of the angle between the conductor and the magnetic field on the magnetic force, and I was wondering about field uniformity. I just want to find out the potential errors that might affect my understanding of my reading.
While it doesn't directly pertain to your question, I would need to know more of your experimental setup. You're using the goniometer to measure the angular displacement; but what is the direction of the current? I'm assuming you're using DC current, because alternating current would yield a fluctuating displacement 180 degrees apart, perpendicular to the direction of current. The amount of displacement depending on the strength of the magnetic field and the amount of current.
So back to your original question, magnetic fields in a permanent magnet are due to the individual magnetic domains within the metal. Not all of the vectors of the fields point in the same direction; consequently, domains on the interior of the magnet will be less affected by outside forces, and point generally in the same direction.
To isolate the amount of deflection, a helmholtz coil should be used of sufficient diameter that the equipment fits within the coils. The coils must be tuned to eliminate the earth's magnetic field and surrounding fields. Then the field of your equipment is the only field affecting the current (except the magnetic field of the current itself, of course).
To study the dependence of the magnetic force with the angle between the current and the magnetic field direction, it is necessary to have, a uniform magnetic field, i.e. a field with induction lines that are straight and also parallel at all points of space.
In a straight permanent magnet, the field is fairly uniform only inside the magnetic body in the vicinity of the center. At all points of the outer region the field is not uniform.
The condition of uniform magnetic field can only be achieved within a long coil having very tight turns. The field lines are quite parallel also in the space between the arms of a horseshoe magnet with a small gap between the arms; here you can have a fairly uniform field. The task of obtaining a uniform magnetic field, for experimental work is quite difficult but, for educational purposes, the horseshoe magnet option is sufficient.
I hope this suggestion will help.