Question

An electron is moving along positive x axis a uniform electric field exists towards negative y axis what should be the direction of magnetic field of suitable magnitude so that net force of electron is zero

Answer 1

Answer:

The direction of the magnetic field must be in negative z-axis

Explanation:

Let the velocity of the electron is v

Then

$\vec v=v\hat i$

If the electric field is E then

$\vec E=-E\hat j$

Lorentz Force

$\vec F=q\vec E+q(\vec v\times \vec B)$

or, $\vec F=-qE\hat j+q(v\hat i\times \vec B)$

For force to be zero

$qE\hat j=q(v\hat i\times \vec B)$

or, $E\hat j=(v\hat i\times \vec B)$

To get the RHS in the direction of $\hat j$, B should be acting in the direction of $-\hat k$. As we know that $\boldsymbol{\hat k\times \hat i=\hat j}$

Therefore the direction of the magnetic field must be in negative z-axis.

Hope this answer is helpful.