Question

A simple model of a hydrogen atom is a positive point charge +e (representing the proton) at the center of a ring of radius a with negative charge −e distributed uniformly around the ring (representing the electron in orbit around the proton). Find the magnitude of the total electric field due to this charge distribution at a point a distance a from the proton and perpendicular to the plane of the ring.

Answer 1

Now e is due to the ring at a

So

We say

1/4πEo(ea/ a²+a²)^3/2

= 1/4πEo ea/2√2a³

So here E is faced towards the ring

Next is E due to a point at the centre

So

E² = 1/4πEo ( e/a²)

Finally we get the total

Et= E²-E

= e/4πEo(2√2-1/2√2)

So the direction here is away from the ring