If a charged particle moves unaccelerated thr | vedclass

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Question

(B) For a charged particle to move unaccelerated,the net Lorentz force acting on it must be zero.$\vec{F}_{net} = q(\vec{E} + \vec{v} 	imes \vec{B})

Vedclass · Accepted Answer

$\vec{v}$ must be perpendicular to $\vec{E}$

Vedclass · Answer

(B) For a charged particle to move unaccelerated,the net Lorentz force acting on it must be zero.$\vec{F}_{net} = q(\vec{E} + \vec{v} 	imes \vec{B}) = 0$This implies $\vec{E} = -(\vec{v} 	imes \vec{B})$.From the properties of the cross product,the vector $(\vec{v} 	imes \vec{B})$ is perpendicular to both $\vec{v}$ and $\vec{B}$.Since $\vec{E} = -(\vec{v} 	imes \vec{B})$,$\vec{E}$ must be perpendicular to both $\vec{v}$ and $\vec{B}$.Therefore,$\vec{v}$ must be perpendicular to $\vec{E}$ is a necessary condition for the force to be balanced in the direction of the electric field.Thus,option $B$ is the correct statement.

If a charged particle moves unaccelerated through a region containing both electric and magnetic fields,which of the following must be true?

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