Work, Energy and Power · Work and kinetic energy

A particle of charge

q

and mass

m

is projected from origin with an initial velocity

\vec v = \left(\dfrac{v_0}{\sqrt2}\hat{\mathrm x} + \dfrac{v_0}{\sqrt2}\hat{\mathrm y}\right)

. There exists a uniform magnetic field

\vec B = B_0\hat{\mathrm z}

and a space varying electric field

\vec E = E_0e^{-\lambda x}\hat{\mathrm x}

within the region

0 \le x \le L

. After travelling a distance such that x-coordinate has changed from

x = 0

x = L

, the change in the kinetic energy is.

(1) $\dfrac{qE_0}{\lambda}\left[1 - e^{-\lambda L}\right]$
(2) $\left(\dfrac{v_0qB_0}{2\lambda}\right)\left[2 - e^{-2\lambda L}\right]$
(3) $\dfrac{qE_0}{\lambda}\left[1 + e^{-\lambda L}\right]$
(4) $q\left[\dfrac{E_0 + v_0B_0}{\lambda}\right]\left[1 - e^{-\lambda L/2}\right]$

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