Question

An electric field of magnitude e is measured at a distance r from a point charge q. if the charge is doubled to 2q, and the electric field is now measured at a distance of 2r from the charge, what is the value of the new electric field?

Answer 1

Electric field is proportional to the charge and inversely proportional to the square of distance:
$E\propto\frac{Q}{r^{2}}$
With charge 2q and distance 2r, the electric field is proportional to:
$E_{q}\propto\frac{2q}{(2r)^{2}}=\frac{2q}{4r^{2}}=\frac{1}{2}\frac{q}{r^{2}}$
The new electric field is half of that of the original measured field.