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A particle of mass \( m \) and charge \( q \) is moving in a region where uniform, constant electric and magnetic fields \( \mathbf{E} \) and \( \mathbf{B} \) are present. E and \( \mathbf{B} \) are parallel to each other. At time \( t=0 \), the velocity \( \mathbf{v}_{0} \) of the particle is perpendicular to \( \mathbf{E} \) (Assume that its speed is always \( c \), the speed of light in vacuum).
\( P \)
W Find the velocity \( v \) of the particle at time \( t \). You must express your answer in terms of \( t, q, m \), the vector \( \mathbf{v}_{0}, \mathbf{E} \) and \( \mathbf{B} \) and their magnitudes \( v_{0}, E \) and \( B \).
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