When the winding c-d of the single-phase, 50 Hz, two winding transformer is supplied from an AC current source of frequency 50 Hz, the rated voltage of 200 V (rms), 50 Hz is obtained at the open-circuited terminals a-b. The cross sectional area of the core is 5000 mm$$^2$$ and the average core length traversed by the mutual flux is 500 mm. The maximum allowable flux density in the core is $$B_{max} = 1$$ Wb/m$$^2$$ and the relative permeability of the core material is 5000. The leakage impedance of the winding a-b and winding c-d at 50 Hz are (5 + j100$$\pi$$ $$\times$$ 0.16) $$\Omega$$ and (11.25 + j100$$\pi$$ $$\times$$ 0.36) $$\Omega$$, respectively. Considering the magnetizing characteristics to be linear and neglecting core loss, the self-inductance of the winding a-b in millihenry is ___________ (Round off to 1 decimal place).

In the figure, the electric field E and the magnetic field B point to x and z directions, respectively, and have constant magnitudes. A positive charge 'q' is released from rest at the origin. Which of the following statement(s) is/are true.

An infinite surface of linear current density $$K = 5{\widehat a_x}$$ A/m exists on the x-y plane, as shown in the figure. The magnitude of the magnetic field intensity (H) at a point (1, 1, 1) due to the surface current in Ampere/meter is ____________ (Round off to 2 decimal places).

The closed curve shown in the figure is described by

$$r = 1 + \cos \theta $$, where $$r = \sqrt {{x^2} + {y^2}} ;x = r\cos \theta ,y = r\sin \theta $$

The magnitude of the line integral of the vector field $$F = - y\widehat i + x\widehat j$$ around the closed curve is ___________ (Round off to 2 decimal places).