# Question about Electric field.

1. The problem statement, all variables and given/known data
A point charge $q_{1}=15.00\mu C$ is held fixed in space. From a horizontal distance of $3.00cm$ , a small sphere with mass $4.00*10^{-3}kg$ and charge $q_{2}=+2.00\mu$C is fired toward the fixed charge with an initial speed of $38.0m/s$ . Gravity can be neglected.
What is the acceleration of the sphere at the instant when its speed is $20.0m/s$ ?
Express your answer with the appropriate units.

2. Relevant equations

$a = \frac{k*q_{1}*q_{2}}{m*r^{2}}$

3. The attempt at a solution

$a = \frac{9*10^{9}*15*10^{-6}*2*10^{-6}}{4*10^{-3}*r^{2}}$

$a = 67.5 * \frac{1}{r^{2}}$

By integration,

$v = -67.5 * \frac{1}{r} + C$

Initial conditions: $v = 38 m/s, r = 0.03m$

$38 = -67.5 * \frac{1}{0.03} + C$

$C = 2288$

$v = -67.5 * \frac{1}{r} + 2288$

When $v = 20m/s$,

$20 = -67.5 * \frac{1}{r} + 2288$

$r = 0.029761904$

$a = 67.5 * \frac{1}{0.029761904^{2}}$

$a ≈ 76200 m/s^{2}$

Since both charges are +ve,

$a = -76200 m/s^{2}$

However, the solution is not correct.

May anyone pointing out the errors? Thank you very much.

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