Positive charge q is distributed uniformly along the x-axis from x = 0 to x = a. a positive point charge q is located on the positive x-axis at x = a + r, where r is the distance to the right end of q.(a) calculate the x-component of the electric field produced by the charge distribution q at points on the positive x-axis where x > a.(b) calculate the y-component of the electric field produced by the charge distribution q at points on the positive x-axis where x > a.(c) calculate the magnitude of the force that the charge distribution q exerts on q.(d) calculate the direction of the force that the charge distribution q exerts on q.

(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.