A particle with charge q moves with a velocit | vedclass

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Question

(A) According to the question, the charge on the particle is $q$ and its velocity is $v$.Due to the uniform electric field, the electric force on the

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) According to the question, the charge on the particle is $q$ and its velocity is $v$.Due to the uniform electric field, the electric force on the particle is $F_{	ext{electric}} = qE$.Due to the uniform magnetic field, the magnetic force on the particle is given by $F_{	ext{magnetic}} = q(v 	imes B)$.For the particle to move undeflected, the net Lorentz force must be zero, which means the electric force and magnetic force must be equal in magnitude and opposite in direction: $F_{	ext{electric}} = F_{	ext{magnetic}}$.Substituting the magnitudes, we get $qE = qvB$.Solving for velocity, we find $v = \frac{E}{B}$.Thus, the condition for the particle to move undeflected is $v = \frac{E}{B}$.

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