In a region of space,a uniform magnetic field | vedclass

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(A) The magnetic field is $\vec{B} = B\hat{j}$. The initial velocity is $\vec{v} = v \cos \alpha \hat{j} + v \sin \alpha \hat{k}$.The magnetic force o

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its $x-$coordinate can never be positive

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(A) The magnetic field is $\vec{B} = B\hat{j}$. The initial velocity is $\vec{v} = v \cos \alpha \hat{j} + v \sin \alpha \hat{k}$.The magnetic force on the proton is $\vec{F} = q(\vec{v} 	imes \vec{B}) = q[(v \cos \alpha \hat{j} + v \sin \alpha \hat{k}) 	imes B\hat{j}] = qvB \sin \alpha (\hat{k} 	imes \hat{j}) = -qvB \sin \alpha \hat{i}$.Since the force is in the negative $x-$direction,the particle will accelerate in the negative $x-$direction. Thus,the $x-$coordinate will always be negative (or zero at the origin). Therefore,the $x-$coordinate can never be positive.

In a region of space,a uniform magnetic field $B$ exists in the $y-$direction. $A$ proton is fired from the origin,with its initial velocity $v$ making a small angle $\alpha$ with the $y-$direction in the $yz$ plane. In the subsequent motion of the proton,

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