Name: Fleming's Left Hand Rule
Uploaded: 2019-07-19
Duration: 2 min 51 s
Description: In this video, we will look at using Fleming’s left-hand rule to help us remember how current, magnetic fields and direction go together. Get in to know more.

Question

Find the force per unit length on two parallel current carrying current.

Accepted Answer

Consider two infinite straight long conductors $P P'$ and $Q Q'$ carrying a current $I_{1}$ and $I_{2}$ respectively in the same direction. They are held parallel and are separated by a distance $d$ in the plane of the paper.

A magnetic field is produced by both the conductors. Since each conductor is in the magnetic field produced by the other, each conductor experiences a force.

Magnetic field at a point on the conductor $P P'$ due to the current $I_{2}$ in the conductor $Q Q'$ is given by

$B_{2} = \frac{μ_{0} I_{2}}{2 π d}$

According to the right-hand thumb rule, the magnetic field $B_{2}$ is perpendicular to the plane of the paper and directed outwards.

Due to this magnetic field, the force on a small length $l$ of the conductor $P P'$ carrying a current $I_{1}$ is given by

$F_{1} = B_{2} I_{1} l \sin 90 ° = B_{2} I_{1} l$

$F_{1} = \frac{μ_{0} I_{2}}{2 π d} I_{1} l = \frac{μ_{0} I_{2} I_{1}}{2 π d} l$

According to Fleming's left-hand rule, the direction of force $F_{1}$ is in the plane of the paper, perpendicular to $P P'$ directed towards $Q Q'$ .

Similarly, the force acting on the conductor $Q Q'$ due to the magnetic field produced by $P P'$ is given by

$F_{2} = \frac{μ_{0} I_{1} I_{2}}{2 π d} l$

The direction of force $F_{2}$ is in the plane of paper, perpendicular to $Q Q'$ directed towards $P P'$ .

Therefore, the force acting on the conductors is equal but acting in opposite directions. Therefore, two linear parallel conductors carrying current in same direction attract each other.

The force per unit length acting on the conductors is given by

$\frac{F}{l} = \frac{μ_{0} I_{1} I_{2}}{2 π d}$

It can be shown that if the current flowing in the two conductors is opposite, then the conductors repel each other.

Find the force per unit length on two parallel current carrying current.

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