Magnetic Field Force Maximum Condition
The force experienced by a current-carrying wire of length L placed in a magnetic field B carrying current I is given by the formula:
$ F = I L B \sin \theta $
Here, F is the magnitude of the force, I is the current in the wire, L is the length of the wire segment within the magnetic field, B is the magnitude of the magnetic field, and θ is the angle between the direction of the current (wire) and the direction of the magnetic field.
Condition for Maximum Force
To find when the force F is maximum, we need to maximize the term \sin θ in the equation.
- The maximum value of the sine function, sin θ, is 1.
- This maximum value occurs when the angle θ is 90 degrees (or $ \frac{\pi}{2} $ radians).
When $ \sin \theta = 1 $, the force equation becomes:
$ F_{max} = I L B $
An angle of θ = 90° means that the wire carrying the current is perpendicular to the magnetic field lines.
Conclusion
Therefore, the wire experiences maximum force when it is perpendicular to the magnetic field.
Important Questions from Magnetic Force on a Current-Carrying Wire
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Which of the statements given above are correct?
