Q11. Del operator is                             .

Q12. Given a vector field, \( \vec{F} = y^2 x \vec{a_x} - yz\vec{a_y} - x^2 \vec{a_z} \), the line integral \( \int{ \vec{F} \cdot \vec{dL} }\) evaluated along a segment on the x-axis from \(x=1\) to \(x=2\) is \(_{-------------}\)

Q13. emf is closed \(_{-------------}\) integral of non-conservational electric field that is generated by battery.

Q14.

Potential at every point on the spherical surface is:

Q15. The direction of electric dipole moment is \(_{-------------}\) applied electric field.

Q16. Displacement current density \(_{-------------}\) current passing through a capacitor.

Q17. A dielectric slab with 500mm x 500mm cross-section is 0.4m long. The slab is subjected to a uniform electric field of \(E = 6a_x + 8a_y\) kV/mm. The relative permittivity of the dielectric material is equal to 2. The value of constant \(\varepsilon_0\) is \(8.85 \times 10^{-12} F/m\) . The energy stored in the dielectric in Joules is \(_{-------------}\)

Q18. Laplacian of a scalar is \(_{-------------}\) .

Q19. Biot Savart law states that

Q20. If \(\bar{r} = x\bar{i} + y\bar{j} + z\bar{k} \) , then, curl \(\bar{r}\) is equal to