The electric field is C. Four times as strong
Explanation:
The magnitude of the electric field around a test charge is given by
where:
is the Coulomb's constant
q is the magnitude of the charge
r is the distance from the charge
We notice that the magnitude of the field is inversely proportional to the square of the distance:
In this problem, we are comparing the field at a distance of
r = 2 mm
with the field at a distance of
r' = 4 mm
So the distance has doubled:
r' = 2r
This means that the new field will be
This means that the field at 4 mm is one fourth as strong as the field at 2 mm: therefore, the field at 2 mm is four times as strong as the field at 4 mm.
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