A thin nonconducting rod with a uniform distribution of positive charge Q is bent into a complete circle of radius R. The central perpendicular axis through the ring is a z axis, with the origin at the center of the ring. What is the magnitude of the electric field due to the rod at (a) z = 0 and (b) z =
[infinity]
? (c) In terms of R, at what positive value of z is that magnitude maximum? (d) If R = 2.00 cm and Q = 4.00 mC, what is the maximum magnitude?

(a). If z = 0, The electric field due to the rod is zero.

(b). If z =  ∞, The electric field due to the rod is .

(c). The positive distance is

(d). The maximum magnitude of electric field is

Explanation:

Given that,

Radius = 2.00 cm

Charge = 4.00 mC

(a). If the radius and charge are R and Q.

We need to calculate the electric field due to the rod

Using formula of electric field

Where, Q = charge

z = distance

If z = 0,

Then, The electric field is

(b). If z = ∞, z>>R

So, R = 0

Then, the electric field is

(c). In terms of R,

We need to calculate the positive distance

If

Then,

Taking only positive distance

(d). If R = 2.00 and Q = 4.00 mC

We need to calculate the maximum magnitude of electric field

Using formula of electric field

Hence, (a). If z = 0, The electric field due to the rod is zero.

(b). If z =  ∞, The electric field due to the rod is .

(c). The positive distance is

(d). The maximum magnitude of electric field is

magnityde and direction

because if the tool that you are using is not balanced it there would be false mass.