Max Electric Field on 4.3mC Ring of Charge: Radius 4cm

[chopticks]

The problem statement: Determine the maximum electric field on the axis of a ring of charge 4.3mC. The radius is 4cm.

I think the key is to use ekvation 1 and derivate to determine the maximum electric field but I'm not sure. Q is the charge, x is axis of the ring, a is the radius. Any suggestion?

 

[Shooting Star]

Correct eqn. Differentiate and equate to zero to get the reqd x.

 

[chopticks]

instead of differentiate, I plot the function in an graph. accodring to the graph there is only on max point where x is approx 0.12m and the electric fields is 4.246*10^18N/C. The electric field is etremley high but since the charge of the ring is 4.3mC it is quite reasonable. Is it physical correct reason?

 

[Shooting Star]

x= a/(sqrt 2) at the pt of maximum.

 

[chopticks]

x= a/(sqrt 2) at the pt of maximum.

now I get the same answer as you=), thanks a lot!