The magnitude of electric field due to a point charge 2q, at distance r is E. Then the magnitude of electric field due to a uniformly charged thin spherical shell of radius R with total charge q at a distance $${r \over 2}(r > > R)$$ will be

The horizontal component of earth's magnetic field at a place is 0.2 G whereas it's total magnetic field is 0.4 G. The angle of dip at the place is

The current in the primary coil of a pair of coils changes from 7 A to 3 A in 0.04 s. The mutual inductance between the two coils is 0.5 H. The induced emf in the secondary coil is -

A square sheet of side 'a' is lying parallel to XY plate at z = a. The electric field in the region is $$\overrightarrow E = c{z^2}\widehat k$$. The electric flux through the sheet is