Question

A charge particle enters into a region containing uniform electric field (E) and uniform magnetic field (B)
along x-axis and y-axis respectively. If it passes the region undeviated, the velocity of charge particle is
given by
N​

Answer 1

Answer:

refer to the attachment

Answer 2

The velocity of the charged particle is given by:

$v_y\hat j+\frac{E}{B}\hat k$

Explanation:

Given

The Electric Field and the Magnetic Field are perpendicular to each other

If the Electric Field is $\vec E=E\hat i$ and the magnetic field is $\vec B=B\hat j$

Let the velocity of  the charged particle be

$\vec v=v_x\hat i+v_y\hat j+v_z\hat k$

If the charge on the particle is q then

The force on the particle

= Force due to electric field + force due to magnetic field

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

$\implies \vec F=q(E\hat i+ (v_x\hat i+v_y\hat j+v_z\hat k)\cross B\hat j)$

$\implies \vec F=q(E\hat i+ v_xB\hat k i-v_z\hat i)$

$\implies \vec F=q(E-v_zB)\hat i+ qv_xB\hat k$

Now if the charged particle passes through the region undeviated then

The force will be zero

i.e. $q(E-Bv_z)=0\implies v_z=\frac{E}{B}$

And $v_x=0$

$v_y$ can have any value

Therefore, the velocity is

$\vec v=v_y\hat j+\frac{E}{B}\hat k$

Hope this answer is helpful.

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