Question

An electron is moving along positive X axis, To get it moving on an anticlockwise circular path in x-y plane, a magnetic field is applied
A. along positive-y axis
B. along positive-z axis
C. along negative-y axis
D. along negative-z axis

Answer 1

Hint:In order to solve this question, we should first know that, electron has a negative charge and when an electron enters in the presence of magnetic field it experiences Lorentz force and here we will use the concept of Lorentz force in order to determine the direction of applied magnetic field.

Complete step by step answer:
If q is the charge which enters in magnetic field B and with a velocity of v then force experienced by charged particle is governed by Lorentz force which is written as $\vec F = q(\vec v \times \vec B)$ and if velocity vector is perpendicular to Magnetic field vector then, the motion governed by charged particles will always be circular path because then velocity, magnetic field and force all three components will be perpendicular to each other.Now, according to the question, we have given that the direction of an electron which has a charge of $q = - e$ is positive X axis which is $\vec v = v\hat i$ where $i$ represent the direction of the velocity vector.

Now electron has to move in anticlockwise manner which shows force acting on electron must be in positive y axis which is $\hat j$ now, using Lorentz force equation, we have $\vec F = q(\vec v \times \vec B)$ indicating directions of various quantities as $\hat j = - e(\hat i \times \hat B)$ and from vector cross product we know that, $\hat i \times \hat k = - \hat j$ and compare this with equation $\hat i \times \hat B = - \hat j$ so direction of magnetic field is positive Z axis which is $\hat k$.

Hence, the correct option is (B).

Note:It should be remembered that, if the direction of force is in X direction then motion of electron will be in clockwise manner and if it were in Z direction then electron will not lies in XY plane, and always check the sign of charge which enters in magnetic field.