A positive charged particle of mass m and charge q is released from rest in a region having E - E0 - and B - B0 - from origin- The net force on the particle at any time t if its velocity at this moment is v - vx - - vz k- -E0 and B0 are constants-

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3rd Equation of Motion

A positive ch...

Question

A positive charged particle of mass $m$ and charge $q$ is released from rest in a region having $\to E = E_{0}^i$ and $\to B = B_{0}^j$ from origin. The net force on the particle at any time $t$ if its velocity at this moment is $\to v = v_{x}^i + v_{z}^k$ :

$[E_{0}$ and $B_{0}$ are constants $]$

q (E_{0} - B_{0} v_{z})^i + q B_{0} v_{x}^k

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q (E_{0} + B_{0} v_{z})^i + q B_{0} v_{x}^k

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q (E_{0} - B_{0} v_{z})^i - q B_{0} v_{x}^k

No worries! We‘ve got your back. Try BYJU‘S free classes today!

q (E_{0} + B_{0} v_{z})^i - q B_{0} v_{x}^k

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Solution

The correct option is A $q (E_{0} - B_{0} v_{z})^i + q B_{0} v_{x}^k$
In this region, the electric field will provide acceleration for the particle in $+ v e$ $x -$ direction and once particle has some velocity in $x -$ direction, the magnetic force will act on it in $+ v e$ $z -$ direction $(^k)$ as per $q (\to v \times \to B)$ .

The particle will translate in $x -$ direction, and it will rotate in $x z$ plane.

At any time $t$ , its velocity can be written as,

$\to v = v_{x}^i + v_{z}^k$

Net force on the particle at this moment will be,

$\to F =_{e} + {\to F}_{m}$

$\Rightarrow \to F = q [E_{0}^i + (v_{x}^i + v_{z}^k) \times B_{0}^j]$

$\Rightarrow \to F = q [E_{0}^i + (B_{0} v_{x})^k - (B_{0} v_{z})^i]$

$\Rightarrow \to F = q (E_{0} - B_{0} v_{z})^i + q B_{0} v_{x}^k$

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A positive charged particle of mass m and charge q is released from rest in a region having →E=E0^i and →B=B0^j from origin. The net force on the particle at any time t if its velocity at this moment is →v=vx^i+vz^k : [E0 and B0 are constants]

A positive charged particle of mass $m$ and charge $q$ is released from rest in a region having $\to E = E_{0}^i$ and $\to B = B_{0}^j$ from origin. The net force on the particle at any time $t$ if its velocity at this moment is $\to v = v_{x}^i + v_{z}^k$ :

$[E_{0}$ and $B_{0}$ are constants $]$