A) angle between \[\mathbf{\vec{v}}\] and \[\mathbf{\vec{B},}\] is necessarily \[{{90}^{\text{o}}}\]
B) angle between \[\mathbf{\vec{v}}\] and \[\mathbf{\vec{B},}\] can have any value other than \[90{}^\circ \]
C) angle between \[\mathbf{\vec{v}}\] and \[\mathbf{\vec{B},}\] can have any value other than zero and \[180{}^\circ \]
D) angle between \[\mathbf{\vec{v}}\] and \[\mathbf{\vec{B},}\] is either zero or \[{{180}^{\text{o}}}\]
Correct Answer: C
Solution :
When a charged particle \[q\] is moving in a uniform magnetic field \[\overrightarrow{B}\] with velocity \[\overrightarrow{v}\] such that angle between \[\overrightarrow{v}\] and \[\overrightarrow{B}\] be \[\theta ,\] then due to interaction between the magnetic field produced due to moving charge and magnetic force applied, the charge q experiences a force which is given by \[F=qvB\,\sin \theta \] If \[\theta =0{}^\circ \]or \[180{}^\circ ,\]then \[\sin \theta =0\] \[\therefore \] \[F=qvB\,\sin \theta =0\] Since, force on charged particle is non-zero, so angle between \[\overrightarrow{v}\] and \[\overrightarrow{B}\] can have any value other than zero and \[180{}^\circ \]. Note: Force experienced by the charged particle is Lorentz force.
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