Question

An electron is traveling along the $x-$direction. It encounters a magnetic field in that $y-$direction. Its subsequent motion will be
A. Straight line along the $x-$direction
B. A circle in the $xz-$plane
C. A circle in the $yz-$plane
D. A circle in the $xy-$plane

Answer 1

Hint: When an electron is traveling along the $x-$direction, it encounters a magnetic field in the $y-$direction. If an $x-$axis and $y-$axis are perpendicular to each other, then the direction of the magnetic force acting on the particle is given by Fleming’s left-hand thumb rule. With the help of this rule, we can easily determine the direction of its subsequent motion.



Formula used:



Complete answer:
Consider the unit vectors in $x,y\And z$ the direction be $\hat{i},\hat{j}\And \hat{k}$. Since it is given, the particle moves along the $x-$axis and the magnetic field $\vec{B}$along the $y-$axis.

Let the electron be moving with velocity,$\vec{v}$. So, the force experienced by a charge $q$ in a uniform magnetic field is
$F=q(\vec{v}\times \vec{B})$
$F=q(v\hat{i}\times B\hat{j})$
Or, $F=-e(v\hat{i}\times B\hat{j})$ [Since the charge of an electron is $-e$]
Or,$F=evB(-\hat{k})$
Hence the force acts in a negative $z-$direction. And it will force electrons to move in a circle in the $xz-$plane.
Now, this can be also understood by Fleming’s left-hand thumb rule.

 According to this rule, if we stretch our forefinger, middle finger, and thumb in such a way that they are mutually perpendicular to each other. Now the fore finger represents the magnetic field along the $y-$ direction and the middle finger shows the direction of the current along the $x-$direction, then the thumb will show the subsequent direction of motion along the $z-$direction.

Thus, the correct option is (B).



Note:According to the right-hand thumb rule, if we arrange our forefinger, middle finger, and thumb perpendicular to each other then the thumb points towards the direction of motion of the conductor relative to the magnetic field when the middle finger points towards the direction of induced current and forefinger towards the direction of the magnetic field.