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Grade: 12

                        

A circular ring carries a charge q the variation if electric field is x measured from centre along axis the maximum electric field on the axis is

5 months ago

Answers : (1)

Arun
24738 Points
							
With C = Q/(4πε₀) the field along the axis is:
 
E = Cx/(x² + R²)^(3/2) (equation 1)
 
This equation can be derived with calculus - see derivation in link for example (short pdf document)
 
When x
 
E ≈ Cx/(R²)^(3/2)
 
. .≈ (C/R³)x
 
(C/R³) is a constant, so this means E varies as (is proportional to) x approximately: E∝x 
 
_________________
 
The maximum electric field occurs at x = x₀ = R/√2 (see the link).
 
Subsititute x = R/√2 in equation 1 giving:
 
Emax = C(R/√2)/((R/√2)² + R²)^(3/2)
 
If you do a bit of algebra to simplify this, it should give the required answer.
5 months ago
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