Question Number 171213 by MikeH last updated on 10/Jun/22
![In electricity, the electrostatic field is defined as: E = ∫_0 ^π [((a^2 σ sin θ)/(2ε(√(a^2 −x^2 −2ax cosθ))))]dθ where a,σ and ε are constants. Consider that x>a and show that E= ((a^2 σ)/(εx))](Q171213.png)
$$\mathrm{In}\:\mathrm{electricity},\:\mathrm{the}\:\mathrm{electrostatic}\:\mathrm{field} \\ $$ $$\mathrm{is}\:\mathrm{defined}\:\mathrm{as}: \\ $$ $${E}\:=\:\int_{\mathrm{0}} ^{\pi} \left[\frac{{a}^{\mathrm{2}} \sigma\:\mathrm{sin}\:\theta}{\mathrm{2}\epsilon\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} −\mathrm{2}{ax}\:\mathrm{cos}\theta}}\right]{d}\theta \\ $$ $$\mathrm{where}\:{a},\sigma\:\mathrm{and}\:\epsilon\:\mathrm{are}\:\mathrm{constants}.\:\mathrm{Consider} \\ $$ $$\mathrm{that}\:{x}>{a}\:\mathrm{and}\:\mathrm{show}\:\mathrm{that}\:{E}=\:\frac{{a}^{\mathrm{2}} \sigma}{\epsilon{x}} \\ $$