Question

What is the force on a current carrying wire that is parallel to the magnetic field? Give reason for your answer.

Answer 1

Moving charges in a magnetic field always experience force. This force is vector quantity and is given as $\overrightarrow F = i(\overrightarrow l \times \overrightarrow B )$
Here F represents the force, i represents the current flowing through the conductor, l represents the length of the conductor and B represents the magnetic field.
This vector notation can be further reduced to $F = ilB\sin \theta$ where $\theta$ is the angle between the elemental current length and the magnetic field.

Formula used:
We shall use the formula for the force experienced by a current carrying conductor when placed in a magnetic field here and deduce our answer from the formula itself.
The mathematical expression for the formula is $F = ilB\sin \theta$ where F represents the force, i represents the current flowing through the conductor, l represents the length of the conductor, B represents the magnetic field and $\theta$ is the angle between the elemental current length and the magnetic field.

Complete step-by-step answer:
Given that the current carrying conductor is placed in the magnetic field such that it is parallel to the direction of the magnetic field.
This means that the angle between the magnetic field and the current carrying conductor is ${0^0}$ .
We know that $\sin {0^0} = 0$
Substituting in the formula we get,
$F = ilB\sin {0^0}$
$\Rightarrow F = 0$
Hence the force acting on a current carrying conductor which is placed parallel to the magnetic field is zero.

Note: The direction of the force experienced by the current carrying conductor when placed in a magnetic field is perpendicular to both magnetic field and the elemental current length. The direction of current is the same as that of the direction of the elemental current length. As a convention we take the elemental current length of the conductor in the formula.