Answer:
(a): .
(b): 0
(c):.
(d): Along positive x axis.
Explanation:
Given that the charge is distributed uniformly on the rod, extended from to and having total charge .
Let be the linear charge density of the rod, such that,
The electric field due to a charge at a point distance away is given by
where is the Coulomb's constant whose value is .
Now consider a small line element of the rod of length at distance from .
The electric field at point due to this element is given by
is the charge on the line charge, then,
Using this value,
The electric field due to the whole rod is given by
This electric is along the x axis only.
(a):
The x component of the electric field at this point = .
(b):
The y component of the electric field at this point = 0.
(c):
The electric field and the electric force are related as
The magnitude of the force that this rod exerts on the charge q = .
(d):
The direction of this force is along the positive x axis.