A particle of specific charge (charge/mass) starts moving from the origin under the action of an electric field ${E = E}_{0}^i$ and magnetic field $B = B_{0}^k$ Its velocity at $(x_{0}, y_{0}, 0)$ is $(4^i - 3^j)$ The value of $x_{0}$

\frac{13 a E_{0}}{2 B_{0}}

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\frac{16 a B_{0}}{E_{0}}

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\frac{25}{2 a E_{0}}

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\frac{5 a}{2 B_{0}}

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Solution

The correct option is A $\frac{13 a E_{0}}{2 B_{0}}$
Electric field $E = E_{0}^i$
magnetic field $B = B_{0}^k$
velocity at $(x_{0}, y_{0}, 0)$ is $(4^i - 3^j)$
Now, speed of the particle at $(x_{0}, 0, 0)$ is $= 5$ unit
Applying work energy theorem and realizing the fact that the magnetic forces do not work give the value of $x_{0}$
$q E_{0} x_{0} = \frac{1}{2} {m V}^{2} = \frac{25 m}{2}$
or, $x_{0} = \frac{1}{2} \frac{13 q E_{0}}{B_{0}}$

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