
Assume Earth’s surface is a conductor with a surface charge density . It rotates about its axis with angular velocity . 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 ( =radius of the earth)
A)
B)
C)
D) Zero
Answer
486.6k+ views
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
Where is the Magnetic field, is the Area, and 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,
Where is the radius of the conductor and is the change in distance.
where = 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
where = radius of the Earth, and = angular velocity of Earth.
Also, the Emf induced at the pole can be given by,
Thus, the resultant Emf induced due to the magnetic field of Earth will be,
Putting in the values we get,
Thus, the emf induced between the pole and the equator of earth is .
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.
Formula Used:
The Emf induced due to the magnetic field is
Where
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,
Where
where
Now, the Emf at the equator, considering the equator as a ring with a radius and an angular velocity, can be written as
where
Also, the Emf induced at the pole can be given by,
Thus, the resultant Emf induced due to the magnetic field of Earth will be,
Putting in the values we get,
Thus, the emf induced between the pole and the equator of earth is
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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