# Force on A Current-carrying Conductor

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When a conductor carrying a current is placed in a magnetic field, the conductor experiences a magnetic force.

• The direction of this force is always right angles to the plane containing both the conductor and the magnetic field, and is predicted by Fleming’s Left-Hand Rule.

Referring to the diagram above, F is Force, B is Magnetic field, I is current.

Factors affecting magnetic force on a current-carrying conductor in a magnetic field:

• Strength of the magnetic field
• Current flowing through the wire
• Length of the wire

$F = B I l \, sin \, \theta$, where

• F is force acting on a current carrying conductor,B is magnetic flux density (magnetic field strength),
• I is magnitude of current flowing through the conductor,
• $l$ is length of conductor,
• $\theta$ is angle that conductor makes with the magnetic field.

When the conductor is perpendicular to the magnetic field, the force will be maximum. When it is parallel to the magnetic field, the force will be zero.

### 36 thoughts on “Force on A Current-carrying Conductor”

1. What if force is halfed effect on magnetic feild

2. This is really good of you people ,I benefit from your contribution

3. Why is sin theta used instead of cos theta when talking about the angle between B and L?

• Because force is a the resultant of B and L is Force which is a vector quantity.

• Can you explain it to me

• Assalamu Alaikum dear brother!
If you put cos instead of sin, force will be zero at 90 angle mathematically but during experiment you will observe that force is acting on conductor and it is not zero. Hence considering cos instead of sin does not make sense. Hope you have got some idea, Thanks!

• because it is a vector product deu to its direction

• as it as vector product so vector angle which is sin is used correspondent to it

4. Drive an expression for the magnitude of the force in a current-carry conductor in a magnetic field.

5. What will be the affect on the magnetic force if we double all the parameters keeping sin 90°?

6. The force on current carrying wire is due to applied magnetic field or its own magnetic induction?

• the external and internal b field interact which result in a magnetic force on a conductor.