# When a charge q is moving in the presence of electric (E) and magnetic (B) fields which are perpendicular to each other and also perpendicular to the velocity v of the particle, write the relation expressing v in terms of E and B.

Let the electric field is Ej, the magnetic field is Bk and velocity is vi then

$\\F=q(v\times B)+qE\\F=-qvB j+qEj\\F=q(E-vB)j$

The force between the electric and magnetic field is opposite. Now if we adjust the force such that the force due to electric and magnetic field are same then the particle moves undeflected.

$\\qE=qvB\\\\v=\frac{E}{B}$

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