A monochromatic beam of light has a frequency $$v = {3 \over {2\pi }} \times {10^{12}}Hz$$ and is propagating along the direction $${{\widehat i + \widehat j} \over {\sqrt 2 }}.$$
It is polarized along the $$\widehat k$$ direction. The acceptable form for the magnetic field is :

An ideal capacitor of capacitance $$0.2\,\mu F$$ is charged to a potential difference of $$10$$ $$V.$$ The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance $$0.5$$ $$mH.$$ The current at a time when the potential difference across the capacitor is $$5$$ $$V,$$ is :

The $$B$$-$$H$$ curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solended with $$1000$$ turns/cm. The current that should be passed in the solended to demagnetise the ferromagnet completely is :

The relative error in the determination of the surface area of sphere is $$\alpha $$. Then the relative error in the determination of its volume is :