hi all
please could you help me how do we integrate this integration in the attachment the answer is bessel function the integration is for loop antenna
thanks
Let $\displaystyle \phi'=A, \phi=B$
$\displaystyle cos(2A)= cos^2A-sin^2A$
$\displaystyle cos(2A)+1= cos^2A-sin^2A+1= 2cos^2A$
$\displaystyle cos(B-A)= cosBcosA-sinBsinA$
Let $\displaystyle jka.sin(\theta)=t$
$\displaystyle e^{t(cos(B-A)}= e^{t(cosBcosA-sinBsinA)}=e^{t(cosBcosA)}\cdot e^{t(sinBsinA)}$
Now try to integrate
$\displaystyle 2cos^2(A)\cdot(e^{t(cosBcosA)}\cdot e^{t(sinBsinA)})dA$