What happens to the electric field at a test charge when the distance between the source charge and the test charge is doubled?
a> the electric field strength is doubled.
b> the electric field strength is halved.
c> the electric field strength is quadrupled.
d> the electric field strength is reduced to one fourth its original value.

The electric field at any distance from a charge is

       E  =  (a constant) · (the size of the charge) / (the distance)² .

-- Notice that the distance is in the denominator, so when the distance
increases, the electric field decreases.

-- Also notice that the distance is squared.  So when the distance increases,
the field doesn't just change as fast as the distance does.  The field drops
as fast as the SQUARE of the distance grows.

If the distance doubles ( · 2 ), the field drops to  (1 / 2²)  =  1/4 .

If the distance triples ( · 3 ), the field drops to  (1 / 3²)  =  1/9 .

If the distance gets 10 times as far, the field drops to  (1 / 10²)  =  1/100 .