Answer
We can rank the three situations according to the magnitude of the electric field at point P:
$(a) \gt (b) \gt (c)$
Work Step by Step
We can write the general expression for the electric field at a point due to a charge:
$E = \frac{1}{4\pi~\epsilon_0}~\frac{q}{r^2}$
We can write the expression for the electric field at point P due to the charge Q in diagram (a):
$E = \frac{1}{4\pi~\epsilon_0}~\frac{Q}{R^2}$
We can consider the electric field at point P in diagram (b).
Note that the net electric field is a vector sum. By symmetry, the vertical component of the electric field from the spread of charges cancels out. The net electric field is directed to the right. However, because the charge is spread at various angles, the magnitude of the electric field in diagram (b) is less than the magnitude of the electric field in diagram (a).
We can consider the electric field at point P in diagram (c).
By symmetry, the electric field is zero.
We can rank the three situations according to the magnitude of the electric field at point P:
$(a) \gt (b) \gt (c)$
