It's fact that where there the most magnetic field lines will exist there will be maximum force on the current carrying conductor...

nd the magnetic field lines r max. near the poles of the magnet... so current carrying conductor must be at its poles... !!!

Introduction:
When a current carrying conductor is placed in a magnetic field, it experiences a force due to the interaction between the magnetic field and the current. This force is known as the magnetic force or the Lorentz force. The direction and magnitude of this force depend on the direction and magnitude of the current and the magnetic field.

Explanation:
The maximum force on a current carrying conductor occurs when the conductor is placed perpendicular to the magnetic field.

When the conductor is perpendicular to the magnetic field, the magnetic force experienced by each charge carrier in the conductor is at its maximum. This is because the angle between the direction of the current and the magnetic field is 90 degrees, resulting in the maximum value of the sine function in the equation for the magnetic force. The magnetic force acts perpendicular to both the current direction and the magnetic field direction.

Mathematical Formulation:
The magnetic force on a current carrying conductor can be calculated using the formula:
F = BILsinθ

Where:
F is the magnetic force,
B is the magnetic field strength,
I is the current flowing through the conductor,
L is the length of the conductor, and
θ is the angle between the current direction and the magnetic field direction.

Direction of the force:
The direction of the force is given by the right-hand rule. If the thumb, forefinger, and middle finger of the right hand are held perpendicular to each other, with the thumb pointing in the direction of the current and the forefinger pointing in the direction of the magnetic field, then the middle finger gives the direction of the force on the conductor.

Conclusion:
In conclusion, the maximum force on a current carrying conductor occurs when the conductor is placed perpendicular to the magnetic field. This is because at this position, the angle between the current direction and the magnetic field direction is 90 degrees, resulting in the maximum magnetic force on the conductor.