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(D) The electron moves along the $+x$ direction,so its velocity vector is $\vec{v} = v\hat{i}$.For the electron to move in an anticlockwise circular p

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$-z$ direction

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(D) The electron moves along the $+x$ direction,so its velocity vector is $\vec{v} = v\hat{i}$.For the electron to move in an anticlockwise circular path in the $x-y$ plane,the centripetal force at the initial position (on the $x$-axis) must be directed towards the $+y$ direction (i.e.,$\vec{F} = F\hat{j}$).The Lorentz force on a charge $q$ is given by $\vec{F} = q(\vec{v} 	imes \vec{B})$.Since the electron has a negative charge $(q = -e)$,we have $\vec{F} = -e(\vec{v} 	imes \vec{B})$.Substituting the known values: $F\hat{j} = -e(v\hat{i} 	imes \vec{B})$.For the cross product $\hat{i} 	imes \vec{B}$ to result in a vector along $-\hat{j}$ (so that $-e(-\hat{j}) = +\hat{j}$),the magnetic field $\vec{B}$ must be along the $-z$ direction (since $\hat{i} 	imes (-\hat{k}) = \hat{j}$,but we need the negative sign from the charge,so $\hat{i} 	imes \hat{k} = \hat{j}$,and with the negative charge,$\vec{F} = -e(v\hat{i} 	imes B\hat{k}) = -evB(-\hat{j}) = +evB\hat{j}$).Thus,the magnetic field must be applied along the $-z$ direction.

An electron is moving along the $+x$ direction. To make it move along an anticlockwise circular path in the $x-y$ plane,the magnetic field must be applied along:

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