A monoenergetic beam of electrons moving alon | vedclass

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(C) The total Lorentz force on the electron is given by $\overrightarrow{F} = -e(\overrightarrow{E} + \vec{v} 	imes \overrightarrow{B})$.For the elec

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$+x$ axis and $+z$ axis

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(C) The total Lorentz force on the electron is given by $\overrightarrow{F} = -e(\overrightarrow{E} + \vec{v} 	imes \overrightarrow{B})$.For the electron to move undeflected,the net force must be zero,i.e.,$\overrightarrow{F} = 0$.This implies $\overrightarrow{E} = -(\vec{v} 	imes \overrightarrow{B}) = \overrightarrow{B} 	imes \vec{v}$.Given the velocity $\vec{v} = v\hat{j}$,if we choose the magnetic field $\overrightarrow{B}$ along the $+x$ direction (i.e.,$\overrightarrow{B} = B\hat{i}$),then the magnetic force is $\vec{F}_m = -e(v\hat{j} 	imes B\hat{i}) = -evB(-\hat{k}) = evB\hat{k}$.To cancel this,the electric force $\vec{F}_e = -e\overrightarrow{E}$ must be in the $-z$ direction,meaning $\overrightarrow{E}$ must be in the $+z$ direction.Thus,for the beam to remain undeflected,the magnetic field $\overrightarrow{B}$ must be along the $+x$ axis and the electric field $\overrightarrow{E}$ must be along the $+z$ axis.

$A$ monoenergetic beam of electrons moving along the $+y$ direction enters a region of uniform electric and magnetic fields. If the beam goes straight undeflected,then fields $B$ and $E$ are directed respectively along:

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