Question

A uniformly charged ring of radius 10.0 cm has a total charge of 66.0 μC. Find the electric field on the axis of the ring at the following distances from the center of the ring. (Choose the x-axis to point along the axis of the ring.) (a) 1.00 cm

Answer 1

To solve this problem we will apply the mathematical consideration of the electric field on an axial axis of a ring. This definition is already established mathematically and is a subordinate of the definition of the magnetic field of Coulomb's laws. It can be expressed as,

$E = \frac{kQx}{\sqrt{(x^2+R^2)^3}}$

Here,

k = Coulomb's constant

Q = Charge

x = Distance on the axial line

R = Radius of the circle or ring

At x = 1 cm, we have that the total charge is 66.0 μC and the radius 0.1m, then replacing,

$E = \frac{(9*10^9)(66*10^{-6})(0.01)}{\sqrt{((0.01)^2+(0.1)^2)^3}}$

$E = 5.85*10^6 N/C$

Therefore the electric field on the axis of the ring is 5.85MN/C