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# A charged particle of mass m and charge q is released from rest from the position $\;(x_{0} ,0)\;$ in a uniform electric field $\;E_{0} \hat{j}\;.$ The angular momentum of particle about origin

$(a)\;zero\qquad(b)\;is\;constant\qquad(c)\;increases\;with\;time\qquad(d)\;decreases\;with\;time$

Answer : (c) increases with time
Explanation :
$\overrightarrow{\Gamma}=\overrightarrow{r}\times\overrightarrow{F}$
$=(x_{0} \hat{i}\times E_{0}\;q\;\hat{j})$
$=E_{0}\;q\;x_{0}\;\hat{k}$
$\large\frac{d L}{dt}=E_{0}\;q\;x_{0}$
$\large\frac{d L}{dt}\;$ is positive i . e . L increases with time .
edited Feb 7, 2014 by yamini.v