(b) If both electric and magnetic fields are present and perpendicular to each other and the particle is moving perpendicular to both of them with $F_{e} = F_{m}$. In this situation $\overrightarrow{\mathbf{E}} \neq 0$ and $\overrightarrow{\mathbf{B}} \neq 0$.
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But if electric field becomes zero, then only force due to magnetic field exists. Under this force, the charge moves along a circle