Consider the time-varying vector $$I = \,\hat x\,\,15\,\cos \,(\omega \,t) + \,\hat y\,5\,sin(\omega \,t)$$ in Cartesian coordinates, where $$\omega $$ > 0 is a constant. When the vector magnitude $$\left| I \right|$$ is at its minimum value, the angle $$\theta $$ that I makes with the x axis (in degree, such that $$0\, \le \,0 \le \,180$$) is _________________

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m² , −4 nC/m² and ρ_s ,respectively. The value of ρ_s (nC/m²) required to ensure that the electric flux density $$\overrightarrow D=\overrightarrow0$$ at radius 10 m is _________.

Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?

In a source free region in vacuum, if the electrostatic potential $$\varphi\;=\;2x^2\;+y^2+cz^2$$ , the value of constant c must be ________________.