JEE Main & Advanced Physics Magnetic Effects of Current / करंट का चुंबकीय प्रभाव Force On a Charged Particle in Magnetic Field

If a particle carrying a positive charge q and moving with velocity v enters a magnetic field B then it experiences a force F which is given by the expression \[\overrightarrow{F}=q(\overrightarrow{v\,}\times \overrightarrow{B})\] \[\Rightarrow \] \[F=qvB\sin \theta \]

where \[\overrightarrow{v\,}\,=\] velocity of the particle, \[\overrightarrow{B}=\] magnetic field

(1) Zero force : Force on charged particle will be zero (i.e. \[F=0\]) if

(i) No field i.e. \[B=0\Rightarrow F=0\]

(ii) Neutral particle i.e. \[q=0\,\Rightarrow F=\text{ }0\]

(iii) Rest charge i.e. \[v=0\,\Rightarrow F=0\]

(iv) Moving charge i.e. \[\theta ={{0}^{o}}\]or \[\theta ={{180}^{o}}\Rightarrow F=0\]

(2) Direction of force : The force \[\overrightarrow{F}\] is always perpendicular to both the velocity \[\overrightarrow{v}\] and the field \[\overrightarrow{B}\] in accordance with Right Hand Screw Rule, though \[\overrightarrow{v}\] and \[\overrightarrow{B}\] themselves may or may not be perpendicular to each other.

Direction of force on charged particle in magnetic field can also be find by Fleming's Left Hand Rule (FLHR).

Here, First finger (indicates) \[\to \]Direction of magnetic field

Middle finger \[\to \] Direction of motion of positive charge or direction, Opposite to the motion of negative charge.

Thumb \[\to \] Direction of force