Force on a Current Carrying Conductor in Magnetic Field

Description:

A current carrying conductor is itself formed by moving charges. Hence, when a current carrying conductor is placed in a magnetic field it experiences a force.

Force on current element Idl→

dF = I→(dl→ × B→)

If V_d = → drift velocity force on Idl→,

dF = (-e)→(V_d→ × B→)

If n is number of e = (-e)→ per unit volume

Total force on volume

⇒ dF = -eAnV_d→(dl→ × B→) ⇒ dF → = I(dl→ × B→)

Direction of magnetic force on wire is determined by

• Right hand palm rule
• Flemings left hand rule

In uniform magnetic field B→

F =→ ∫ I(dl→ × B→) = I ∫ (dl → ×B→)

F =→ I(I→ × B→)