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Assume Earth’s surface is a conductor with a surface charge density σ. It rotates about its axis with angular velocity ω. Suppose the magnetic field due to the Sun at Earth at some instant is a uniform field B pointing along Earth’s axis. Then the emf developed between the pole and the equator of the earth due to this field is (Re=radius of the earth)
A) 12BωRe2
B) BωRe2
C) 32BωRe2
D) Zero

Answer
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Hint: The induced Emf has to be calculated. The induced Emf due to a magnetic field calculated at different points of Earth will be different. This will solve your current problem.

Formula Used:
The Emf induced due to the magnetic field is
Emf=BAt
Where B is the Magnetic field, A is the Area, and t is the change in time.

Complete step by step answer:
When a conductor is passed inside a magnetic field, an EMF is generated and the reaction caused due to the magnetic field induced in the conductor with the original magnetic field causes deflection.
Using Faraday's Law we have,
Induced EMF is given as the rate at which magnetic flux changes in time.
Induced EMF = (change in Magnetic Flux Density x Area)/change in Time.
Which can also be written as,
Emf=BAt
A=R2Δx
Where R is the radius of the conductor and Δx is the change in distance.
Emf=BR2Δxt
Emf=BR2Δxt
Emf=BR2ω
where ω= the angular velocity of Earth.
Now, the Emf at the equator, considering the equator as a ring with a radius and an angular velocity, can be written as
EmfE=BRe2ω
where Re= radius of the Earth, and ω= angular velocity of Earth.
Also, the Emf induced at the pole can be given by,
Emf=BRe2ω
Emf=B×0×ω
EmfP=0
Thus, the resultant Emf induced due to the magnetic field of Earth will be,

EmfT=EmfEEmfP2
Putting in the values we get,
EmfT=EmfEEmfP2
EmfT=BRe2ω02
EmfT=12BRe2ω

Thus, the emf induced between the pole and the equator of earth is 12BRe2ω.

Hence, option (A) is the correct answer.

Note:
When we are solving a problem like this, we have to first visualize the object to get a clear picture. Then we have to calculate the parameter at the individual points. Subsequently by subtracting we get the final answer.
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