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

AI Thread Summary
To determine the maximum electric field on the axis of a ring of charge with a total charge of 4.3mC and a radius of 4cm, the key is to differentiate the electric field equation and set it to zero to find the optimal position along the axis. A graphical approach also confirms that the maximum occurs at approximately 0.12m, yielding an electric field strength of 4.246 x 10^18 N/C. This value is considered reasonable given the charge of the ring. The relationship x = a/(sqrt 2) is validated as the point of maximum electric field. The discussion concludes with agreement on the calculated results.
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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?
 

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Correct eqn. Differentiate and equate to zero to get the reqd x.
 
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?
 
x= a/(sqrt 2) at the pt of maximum.
 
Shooting star said:
x= a/(sqrt 2) at the pt of maximum.

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