The coercivity of a small magnet where the ferromagnet gets demagnetized is $$3 \times {10^3}\,A{m^{ - 1}}.$$ The current required to be passed in a solenoid of length $$10$$ $$cm$$ and number of turns $$100,$$ so that the magnet gets demagnetized when inside the solenoid, is :

A conductor lies along the $$z$$-axis at $$ - 1.5 \le z < 1.5\,m$$ and carries a fixed current of $$10.0$$ $$A$$ in $$ - {\widehat a_z}$$ direction (see figure). For a field $$\overrightarrow B = 3.0 \times {10^{ - 4}}\,{e^{ - 0.2x}}\,\,{\widehat a_y}\,\,T,$$ find the power required to move the conductor at constant speed to $$x=2.0$$ $$m$$, $$y=0$$ $$m$$ in $$5 \times {10^{ - 3}}s.$$ Assume parallel motion along the $$x$$-axis.

A thin convex lens made from crown glass $$\left( {\mu = {3 \over 2}} \right)$$ has focal length $$f$$. When it is measured in two different liquids having refractive indices $${4 \over 3}$$ and $${5 \over 3},$$ it has the focal lengths $${f_1}$$ and $${f_2}$$ respectively. The correct relation between the focal lengths is :

Two beams, $$A$$ and $$B$$, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $$A$$ has maximum intensity (and beam $$B$$ has zero intensity), a rotation of polaroid through $${30^ \circ }$$ makes the two beams appear equally bright. If the initial intensities of the two beams are $${{\rm I}_A}$$ and $${{\rm I}_B}$$ respectively, then $${{{{\rm I}_A}} \over {{{\rm I}_B}}}$$ equals: