A particle of charge q and mass m is subjected to an electric field
E = E0
(1 – $a$x2) in the x-direction,
where $a$ and E0
are constants. Initially the particle was at rest at x = 0. Other than the initial
position the kinetic energy of the particle becomes zero when the distance of the particle from the
origin is :
Solution
$W = \Delta KE$
<br><br>As inital and final kinetic energy both are zero so $\Delta KE$ = 0
<br><br>$\therefore$ W = 0
<br><br>$\Rightarrow$ $\int\limits_0^x {Fdx} = 0$<br><br>$\Rightarrow$ $q\int\limits_0^x {{E_0}\left( {1 - a{x^2}} \right)dx} = 0$<br><br>$\Rightarrow$ $q{E_0}\left[ {\int\limits_0^x {dx - a} \int\limits_0^x {{x^2}dx} } \right] = 0$<br><br>$\Rightarrow$$q{E_0}\left[ {x - {{a{x^3}} \over 3}} \right] = 0$<br><br>$\Rightarrow$ $x\left( {1 - {{a{x^2}} \over 3}} \right) = 0$<br><br>$\Rightarrow$ $x = 0,$ ${1 - {{a{x^2}} \over 3}}$ = 0<br><br>$\Rightarrow$ ${{{a{x^2}} \over 3}}$ = 1<br><br>$\Rightarrow$ ${x = \sqrt {{3 \over a}} }$
About this question
Subject: Physics · Chapter: Electrostatics · Topic: Coulomb's Law
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