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(D) For a particle to pass undeflected through a region with both electric field $\vec{E}$ and magnetic field $\vec{B}$,the net Lorentz force must be

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both $B$ and $E$ are doubled in magnitude.

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(D) For a particle to pass undeflected through a region with both electric field $\vec{E}$ and magnetic field $\vec{B}$,the net Lorentz force must be zero.The net force is given by $\vec{F} = q(\vec{E} + \vec{v} 	imes \vec{B}) = 0$.This implies $\vec{E} = -(\vec{v} 	imes \vec{B})$.If both the magnitude of the electric field $E$ and the magnetic field $B$ are doubled,the new electric field becomes $E' = 2E$ and the new magnetic field becomes $B' = 2B$.The new force equation becomes $\vec{F}' = q(2\vec{E} + \vec{v} 	imes 2\vec{B}) = 2q(\vec{E} + \vec{v} 	imes \vec{B})$.Since the original condition was $\vec{E} + \vec{v} 	imes \vec{B} = 0$,the new force $\vec{F}'$ remains zero. Thus,the particle continues to pass undeflected.

$A$ particle of charge $q$ and velocity $v$ passes undeflected through a space with non-zero electric field $E$ and magnetic field $B$. The undeflected condition will hold if:

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