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(B) The net force on a charged particle moving in a region of electric field $\overrightarrow{E}$ and magnetic field $\overrightarrow{B}$ is given by

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(B) The net force on a charged particle moving in a region of electric field $\overrightarrow{E}$ and magnetic field $\overrightarrow{B}$ is given by the Lorentz force equation: $\overrightarrow{F} = q(\overrightarrow{E} + \overrightarrow{v} 	imes \overrightarrow{B})$.For the net force to be zero,we must have $\overrightarrow{F} = 0$,which implies $\overrightarrow{E} = -(\overrightarrow{v} 	imes \overrightarrow{B})$.This means the electric force $\overrightarrow{F_e} = q\overrightarrow{E}$ and the magnetic force $\overrightarrow{F_m} = q(\overrightarrow{v} 	imes \overrightarrow{B})$ must be equal in magnitude and opposite in direction.In Figure $B$,the velocity $\overrightarrow{v}$ is along the $x$-axis,the magnetic field $\overrightarrow{B}$ is along the $z$-axis,and the electric field $\overrightarrow{E}$ is along the $y$-axis.The magnetic force $\overrightarrow{F_m} = q(\overrightarrow{v} 	imes \overrightarrow{B})$ will be in the direction of $(\hat{i} 	imes \hat{k}) = -\hat{j}$,which is along the negative $y$-axis.The electric force $\overrightarrow{F_e} = q\overrightarrow{E}$ is along the positive $y$-axis.Since the forces are opposite in direction,they can cancel each other out if their magnitudes are equal $(|qE| = |qvB|)$. Thus,the net force can be zero in Figure $B$.

$A$ particle of charge $q$ and mass $m$ is moving along the $x$-axis with a velocity $v$ and enters a region of electric field $E$ and magnetic field $B$ as shown in the figures below. For which figure may the net force on the charge be zero?

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