If a charged particle travels without acceleration in a region containing electric and magnetic fields,

Step-by-step solution

The Lorentz force on a charged particle is given by F = q( E + v B ) . For the particle to move without acceleration, the net force must be zero: q( E + v B ) = 0 E = -( v B ) = B v From the properties of the cross product, the vector E must be perpendicular to both B and v . Therefore, E B and v E . The magnitude of the electric field is E = vB , where is the angle between v and B . Thus, E is not necessarily equal to vB , and v is not necessarily perpendicular to B .