Q3 (a) In electrostatics, the electric field lines can't form any closed loops. However, the electric field lines in electrodynamics formed closed loops, which is entirely based on Green's theorem such as relation between integral and differential forms of Maxwell equations and the energy of steady currents. Solve the following line integrals using Green's Theorem based on the above condition: (1+ xy?)ax - x y ay where C consists of the are of the parabola y = x from (-1, 1) to (1, 1). ii. fix y ax - xy ay where C is the circle x? + y? = 4. C (b ) Ifj V . Fav = [[ F. QA Let S be a sphere of radius R while V is the solid ball filling that sphere, and let F(x, y, z) = e"i + In(xy)j+ ek be a spherically symmetric radial vector field. Determine: 1 . Divergence at point (0, 1, 1). ii. Curl at point (1, 0, 0)