Question

A ball of mass $2kg$ having charge $1\mu C$ is dropped from the top of a high tower. In the space, an electric field exist in horizontal direction away from the tower which varies as $E=(5-2x)\times {10}^{6}V/m$ (where $x$ is horizontal distance from tower), the maximum horizontal distance (in $m$) ball can go from the tower is

Answer 1

As the charged ball drops from the tower, due to presence of electric field a force starts to act on it. This force is in the direction of electric field and pushes the ball away from the tower or towards the tower depending upon $x$.
The force is given by, $F_x=qE$

$F_x=(1\times {10}^{-6})(5-2x)\times {10}^6{F}_x=5-2x$

This force causes horizontal acceleration of the ball given by,
$a_x=\frac{F_x}{m}=\frac{5-2x}{2}=2.5-x$

This implies, the body performs SHM, with a mean position equal to $2.5m$

The body is released at $x=0$ and the mean position is at $x=2.5$, so the other extreme point is at $5m$.