Figure shows a square loop of edge `a` made of a uniform wire. A current `i` enters the loop at the point A and leaves it at the point C. Find the magnetic field at the point P which is on the perpendicular bisector of AB at a distance a/4 from it. `

Explanation

Magnetic field at point P due to part AD =-magnetic field due
to part BC
`implies vecB_(AD)=-vecB_(BC) implies vecB_(AD)+vecB_(BC)=0`
`vecB_(AB)=(mu_0(i//2))/(4pi(a//4))(sin theta_1+sin theta_2) odot`

`=(u_0i)/(2pia)((a//2)/(asqrt5//4)+(a//2)/(asqrt5//4)) odot`
`=(mu_0i)/(2pia)xx2xxa/2xx4/(asqrt5) odot=(2mu_0i)/(sqrt5 pia)odot`
`:. vecB_(CD)=(mu_0(i//2))/(4pia(3a//4))(sin theta_3+sin theta_4)ox`
`=(mu_0(i//2))/(3pia)xx2xxa/2xx4/(asqrt13) ox=(2mu_0i)/(sqrt13 pia)ox`
`:. vecB_("net")=(2mu_0i)/(pid)(1/sqrt5-1/(3sqrt13))odot`