An electron is moving along the positive x-ax | vedclass

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(B) The net force on the electron is given by the Lorentz force equation: $\vec{F}_{net} = \vec{F}_{e} + \vec{F}_{m} = 0$.Since $\vec{F}_{e} = q\vec{E

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negative $z$-axis

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(B) The net force on the electron is given by the Lorentz force equation: $\vec{F}_{net} = \vec{F}_{e} + \vec{F}_{m} = 0$.Since $\vec{F}_{e} = q\vec{E}$ and $\vec{F}_{m} = q(\vec{v} 	imes \vec{B})$,we have $q\vec{E} + q(\vec{v} 	imes \vec{B}) = 0$,which simplifies to $\vec{E} + (\vec{v} 	imes \vec{B}) = 0$.Given $\vec{v} = v\hat{i}$ and $\vec{E} = -E\hat{j}$,substituting these into the equation gives: $-E\hat{j} + (v\hat{i} 	imes \vec{B}) = 0$,or $v\hat{i} 	imes \vec{B} = E\hat{j}$.For the cross product of $\hat{i}$ and $\vec{B}$ to result in $\hat{j}$,the vector $\vec{B}$ must be along the negative $z$-axis $(-\hat{k})$,because $\hat{i} 	imes (-\hat{k}) = \hat{j}$.Thus,the magnetic field must be directed along the negative $z$-axis.

An electron is moving along the positive $x$-axis. $A$ uniform electric field exists towards the negative $y$-axis. What should be the direction of a magnetic field of suitable magnitude so that the net force on the electron is zero?

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