A particle of charge q and mass m is projected from origin with an initial velocity \(\vec{v}=\left(\frac{{v}_{0}}{\sqrt…

A particle of charge q and mass m is projected from origin with an initial velocity \(\vec{v}=\left(\frac{{v}_{0}}{\sqrt{2}}x+\frac{{v}_{0}}{\sqrt{2}}y\right).\) . There exists a uniform magnetic field \(\vec{B}={B}_{0}\overset{^}{z}\) and a space varying electric field \(\vec{E}={E}_{\mathrm{o}}{\mathrm{e}}^{-\lambda x}\overset{^}{x}\) within the region \(0⩽x⩽L\) After travelling a distance such that x-coordinate has changed from x = 0 to x = L, the change in the kinetic energy is______ .

[JEE Main 2026, 5 Apr (Shift 2)]