SEE,

THE FORCE EXPERIENCED BY ANY CHARGE KEPT x DISTANCE AWAY FROM A CONDUCTING PLATE IS GIVEN BY

 

 NOW, SUPPOSE  THIS PARTICLE IS MOVED BY A SMALL DISTANCE dx.

THEREFORE, THE WORK DONE WILL BE

NOW INTEGRATE THIS  FROM L TO INFINITY THT IS

AND U WILL GET THE ANSWER AS

I THINK THIS IS THE REQUIRED ANSWER AND PROBABLE SOLUTION.

RATE  IF SATISFIED OR U CAN ASK FOR FURTHER EXPLANATION.

PLZ.... RATE