GATE 2017 EC (EC2) – Question 63
An electron q1 moves in free space at $10^5$ m/s toward a stationary electron q2 far away. The closest distance reached before repulsion diverts the moving electron is ________ $\times10^{-8}$ m. Given $m=9.11\times10^{-31}$ kg, $e=-1.6\times10^{-19}$ C and $\epsilon_0=(1/36\pi)\times10^{-9}$ F/m.
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Correct answer: 4.55 to 5.55
Explanation
Under the fixed-stationary-target interpretation used by the official key, the incident electron's initial kinetic energy converts into electrostatic potential energy at the turning point:
$$\tfrac12mv^2=\frac{e^2}{4\pi\epsilon_0r}.$$
Here $1/(4\pi\epsilon_0)=9\times10^9$. Therefore $r=2(9\times10^9)(1.6\times10^{-19})^2/[9.11\times10^{-31}(10^5)^2]=5.058\times10^{-8}$ m.
The requested coefficient is **5.06**, within the official 4.55–5.55 interval.
This calculation holds q2 stationary. If both electrons were free to recoil, center-of-mass motion would have to be retained and the closest separation would be twice this value; the wording does not state a target constraint explicitly.