Question

What are the factors on which the force acting on a given current-carrying conductor placed in a magnetic field depends? State when the magnitude of force is highest.

Answer 1

Hint : We use the formula for the force acting on a current carrying wire in a magnetic field and see which of the factors are influencing the magnitude of force. The direction of the force acting on the wire is given by Fleming's left hand rule.

Formula used: Force acting on current carrying wire $ F = BiL\sin \theta $
Here, Force is represented by $ F $, $ B $ is the magnitude of the uniform magnetic field, $ i $ is the current in the conductor, $ L $ is the Length of the current carrying wire, $ \theta $ is the angle between the current flowing in the conductor and the magnetic field.

Complete step by step answer
From the formula of force acting on current carrying conductor $ F = BiL\sin \theta $
We can see that all with increasing values of $ B,i,L $ force acting on the current carrying conductor increases.
Also, with increasing value of $ \sin \theta $ force value increases.
Hence, force depends on
-the magnitude of magnetic field it is present in
-Current flowing in the conductor
-Length of the conductor
-Angle made by the magnetic field and the current flow in the conductor
We know that the range of $ \sin \theta $ is from $ 0 $ to $ 1 $ hence when $ \sin \theta $ is $ 1 $ force is maximum. Which means $ \theta $ should be $ 90^\circ $
Hence when the direction of magnetic field and the current flowing in the conductor are perpendicular to each other the force acting on the conductor in the magnetic field is highest.

Note
Students often get confused with the length of the conductor and the cross-sectional area of the conductor. Force depends on length and not cross-sectional area. Fleming's left hand rule tells us that direction at which the force is acting on the wire. It gives a relation between the directions of force acting on conductor, magnetic field and current in the conductor.