Question

The magnitude and direction of force on current carrying wire is

(1) $BIL\left( { - \hat j} \right)$
(2) $BIL\left( {\hat j} \right)$
(3) $BIL\left( { - \hat i} \right)$
(4) Zero

Answer 1

Use the concept that the magnitude of the force on current-carrying wire depends on the magnetic field lines, length of the wire, and the current flowing in the wire. We can determine the direction of the force with the help of Fleming's left-hand rule.

Complete step by step answer:
Suppose we placed a current-carrying wire of length L in the magnetic field, then magnetic force acts on the wire, and the magnitude of the magnetic force depends on the position of the current-carrying wire if the wire is placed in such a way that the magnetic field lines and wire are perpendicular to each other then in this condition. In that case, the magnitude of the force is highest.
But if we placed the current-carrying wire at some angle with respect to the magnetic field lines, then the force's magnitude varies and depends on the angle at which the wire is placed. If the angle's value is more, then the force's magnitude becomes more, and if the angle is small, the magnitude of the force becomes small. If we place the current-carrying wire parallel to the direction of magnetic field lines, then the magnitude of the force becomes zero. In the given figure, it is visible that the magnetic field lines are parallel to the wire, so the force's magnitude will become zero.Therefore, the force's magnitude and direction on the current-carrying wire is zero, and option (4) is correct.

Note: When the magnetic field lines are parallel to the current-carrying wire, we can not use the Fleming left-hand rule to determine the direction of the force because when the magnitude of the force becomes zero, then no force is present on the wire.