Question

The electric field at the center of a ring of charge is zero. At very large distances from the center of the ring along the ring's axis the electric field goes to zero. Find the distance from the center of the ring along the axis (perpendicular to the plane containing the ring) at which the magnitude of the electric field is a maximum. The radius of the ring is 7.55 cm and the total charge on the ring is 7.06E-6 C.

Answer 1

Answer:b
`4.29* 10^6\ N/C`

Step-by-step explanation:

Given

The radius of the ring is
`a=7.55\ cm`

The charge on the ring is
`Q=7.06* 10^(-6)\ C`

Electric field along the axis at a distance
`x` is given by

`E=\frac{kxQ}{(x^2+a^2)^{(3)/(2)}}`

To get the maximum value, differentiate
`E` w.r.t
`x` we get

`E_(max)=(2kQ)/(3√(3)a^2)\quad [\text{at}\ x=(a)/(√(2))]\\\\E_(max)=(2* 9* 10^9* 7.06* 10^(-6))/(3√(3)(7.55* 10^(-2))^2)\\\\E_(max)=(24.456* 10^3)/(57* 10^(-4))=4.29* 10^6\ N/C`