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