CATAGORY: Electricity & Magnetism
QUESTION: Two charged particle are at rest near one another, a small
positve
charge on the left and a much larger negative charge on the right.
There is a point near the charges where the electric field due to
the two of them is zero. Is it between the charges, to the left of
the positive charge or to the right of the negative charge? Explain
answer and give reasoning.

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Here is the arrangement. 
                                       
            +q                -Q        
 
  <---       |       --->      |    ---> direction of +q field               
            
  --->       |       --->      |    <--- direction of -Q field                
         
We will consider the electric field on the x axis only. 

(i) Inbetween the two charges the electric field of the +q charge
points to the right (Field lines originate on + charges.)  and the
electric field of the -Q charge points to the right as well (Field
lines terminate on - charrges.).  Thus inbetween the two charges the
electric field of both points to the right so they can never cancel in
this region.

(ii) To the right of the -Q charge the +q charge produces an electric
field which is pointed to the right but the -Q charge produces a field
pointed to the left.  The magnitude of the field due to the -Q charge
is always larger than the field due to the the +q charge in this
region because (a) the |-Q|>|+q| and (b) the distance from any point
to the right of the -Q from the charge -Q is always less than the
distance to +q and the electric field is proportional to
1/(distance)^2.  Thus the magnitude of the electric field of the -Q
charge is always greater than the +q charge so the electric fields
can never cancel.

(iii) To the left of the +q charge the fields can cancel because
the field from the +q charge points to the left and the -Q charge
points to the right and because the distance to the +q charge is
always smaller than the -Q charge so that if we get close enough to
the +q charge the electric field due to it will be large enough to
cancel the field of the farther -Q charge.