If a charged particle moves in a gravity-free | vedclass

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Question

(B) The force on a charged particle $q$ moving with velocity $\overrightarrow{v}$ is given by the Lorentz force law: $\overrightarrow{F} = q(\overrigh

Vedclass · Accepted Answer

$\overrightarrow{E} 
eq 0, \overrightarrow{B} = 0$

Vedclass · Answer

(B) The force on a charged particle $q$ moving with velocity $\overrightarrow{v}$ is given by the Lorentz force law: $\overrightarrow{F} = q(\overrightarrow{E} + \overrightarrow{v} 	imes \overrightarrow{B})$.For the particle to move with uniform velocity,the net force must be zero,i.e.,$\overrightarrow{F} = 0$.Case $A$: If $\overrightarrow{E} = 0$ and $\overrightarrow{B} = 0$,then $\overrightarrow{F} = 0$. This is possible.Case $B$: If $\overrightarrow{E} 
eq 0$ and $\overrightarrow{B} = 0$,then $\overrightarrow{F} = q\overrightarrow{E}$. For $\overrightarrow{F} = 0$,we need $\overrightarrow{E} = 0$,which contradicts the assumption. Thus,this is not possible.Case $C$: If $\overrightarrow{E} = 0$ and $\overrightarrow{B} 
eq 0$,then $\overrightarrow{F} = q(\overrightarrow{v} 	imes \overrightarrow{B})$. If $\overrightarrow{v}$ is parallel or anti-parallel to $\overrightarrow{B}$,then $\overrightarrow{v} 	imes \overrightarrow{B} = 0$,so $\overrightarrow{F} = 0$. This is possible.Case $D$: If $\overrightarrow{E} 
eq 0$ and $\overrightarrow{B} 
eq 0$,it is possible to have $\overrightarrow{E} = -(\overrightarrow{v} 	imes \overrightarrow{B})$ such that $\overrightarrow{F} = 0$. This is possible.Therefore,option $B$ is not possible.

If a charged particle moves in a gravity-free space with uniform velocity,then which of the following is not possible? ($\overrightarrow{E} =$ electric field,$\overrightarrow{B} =$ magnetic field)

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