$($GRADUATE STUDENTS ONLY$)4\mathrm{.}14($a$)$ Consider that two infinitely long parallel positive edge

dislocations are viewed on a simple two$-$dimensional $x,y$ diagram such as Fig. $4\mathrm{.}36.$ One

dislocation is located at $x=0,y=0.$ Since this is a positive edge, its slip plane is horizontal and

contains the $x$ axis. The other dislocation also lies in a horizontal slip plane but this plane is

separated from that of the first dislocation by a vertical distance $(y)$ of $10b,$ where $b$ is the Burgers

vector for both dislocations. Now assume the first dislocation is fixed in place and the second can

move parallel to the $x$ axis. With the aid of a computer, plot $Fx,$ the $x$ component of the force $($per

unit $($ength$)$ between the dislocations, as a function of $x$ from $x=-240nm$ to $x=240nm.$ Let $=86$

GPa, $b=0\mathrm{.}248nm,$ and $v=0\mathrm{.}3.(15$ pts $)$

$($b$)$ Discuss the significance of the variation of $F$ with distance as the mobile dislocation is moved

from $x=-$ to $=+.(5$ pts$)$