Assume Earth's surface is a conductor with a uniform surface charge density `sigma`. It rotates about its axis with angular velocity `omega`. Suppose the magnetic field due to Sun at Earth at some instant is a uniform field B pointing along earth's axis. Then the emf developed between the pole and equator of earth due to this field is. (`R_e =`radius of earth)

Options

A. `1/2 B omegaR_(e)^(2)`
B. ` B omegaR_(e)^(2)`
C. `3/2 B omegaR_(e)^(2)`
D. zero

Explanation

the equator can be seen as a conducting ring of raduis `R_(e)` revolving with angular velocity `omega` in perpendicular magnetic field B.
`:.` Potential difference across its centre and periphery `=(B omegaR_(e)^(2))/2`
Potential at pole =potential of the axis of earth i.e. potential at point O
`:. V_("equator")-V_("Pole")=(B omegaR_(e)^(2))/2`