A particle of charge q and mass m starts moving from the origin with a velocity vecv=v0 hatj under the action of an electric field vecE=E0 hati and magnetic field vecB=B0 hati. The speed of the particle will become 2 v0 after a time t=(√x ⋅ m v0/q E0) . Find the value of x.

Question

A particle of charge q and mass m starts moving from the origin with a velocity vecv=v0 hatj under the action of an electric field vecE=E0 hati and magnetic field vecB=B0 hati. The speed of the particle will become 2 v0 after a time t=(√x ⋅ m v0/q E0) . Find the value of x. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/13fae8810dcd2d181558c9a1c94cefa4-.png" /> Let the velocity of particle along x-axis be vx. ⇒ √v02+vx2=2 v0 vx=√3 v0 ax=(q E0/m) ⇒ vx=ax t ⇒ √3 v0=(q E0 t/m) ⇒ t=(√3 v0 m/q E0)

Q. A particle of charge q and mass m starts moving from the origin with a velocity v=v0​j^​ under the action of an electric field E=E0​i^ and magnetic field B=B0​i^. The speed of the particle will become 2v0​ after a time t=qE0​x​⋅mv0​​. Find the value of x.

Let the velocity of particle along x-axis be vx​. ⇒v02​+vx2​​=2v0​ vx​=3​v0​ ax​=mqE0​​ ⇒vx​=ax​t ⇒3​v0​=mqE0​t​ ⇒t=qE0​3​v0​m​

Let the velocity of particle along $x$ -axis be $v_{x}$ .
$\Rightarrow v_{0}^{2} + v_{x}^{2} = 2 v_{0}$
$v_{x} = 3 v_{0}$
$a_{x} = \frac{q E _{0}}{m}$
$\Rightarrow v_{x} = a_{x} t$
$\Rightarrow 3 v_{0} = \frac{q E _{0} t}{m}$
$\Rightarrow t = \frac{3 v _{0} m}{q E _{0}}$