1. Tardigrade
  2. Question
  3. Physics
  4. In a certain region, uniform electric field E and magnetic field B are present in the opposite direction. A particle of mass m and of charge q enters in this region with a velocity v at an angle θ from the magnetic field. The time after which the speed of the particle would be minimum is equal to

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Q. In a certain region, uniform electric field $E$ and magnetic field $B$ are present in the opposite direction. A particle of mass $m$ and of charge $q$ enters in this region with a velocity $v$ at an angle $\theta $ from the magnetic field. The time after which the speed of the particle would be minimum is equal to

NTA AbhyasNTA Abhyas 2020Moving Charges and Magnetism

Solution:

The charges experiences a retarding force $F=qE$ along x-axis
Retardation $=\frac{q E}{m}$ .
Solution
It is clear that the speed of the particle will be minimum when its component of velocity is along the direction of electric field.
Then, using the equation of motion,
$v=u+at$
$\Rightarrow \, 0=vcos \theta -\frac{q E}{m}t$
$\Rightarrow \, t=\frac{m v cos \theta }{q E}$