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# A particle of specific charge (charge/mass) α starts moving from the origin under the action of an electric field $E_0 \hat i$ and a magnetic field $B_0 \hat k$ . Its velocity at $(x_0, 0, 0)$ is $4 \hat i + 3 \hat j$. The value of $x_0$ is

$\begin {array} {1 1} (a)\;\large\frac{13 q E_0}{2B_0} & \quad (b)\;\large\frac{8B_0}{ q E_0} \\ (c)\;\large\frac{25}{2 q E_0} & \quad (d)\;\large\frac{8q}{B_0} \end {array}$

Speed of the particle at $(x_0, 0, 0)$ is 5 units
Applying work-energy theorem and realising the fact that the magnetic forces do no work give the value of $x_0$
$qE_0x_0 = \large\frac{1}{2} mv^2 = \large\frac{25m}{2}$
Ans : (c)