Earth has a magnetic dipole moment of 8.0 10 22 J / T. Find the magnitude of current in a single turn of wire extending around Earth at its geomagnetic equator to produce a dipole having the same dipole moment. Could such an arrangement be used to cancel out Earth's magnetism?

Question

Earth has a magnetic dipole moment of   8.0         10          22           J      /    T. Find the magnitude of current in a single turn of wire extending around Earth at its geomagnetic equator to produce a dipole having the same dipole moment. Could such an arrangement be used to cancel out Earth&#039;s magnetism?

notemilyu1208 · Accepted Answer

a)The expression for the magnetic dipole moment is written as,  M  =  I  A  …  (  1  )Here, I and A represent the magnitude of current and the cross-section area of a loop, respectively.Step 2The cross-section area of a loop will be,  A  =  π      r    2  Here, r represents the radius of the Earth.The radius of the Earth is around 6370 km.Therefore,  A  =  π  (  6370  ×      10    3       m      )    2      =  1.274  ×      10          14               m    2  Step 3Substitute all the known values in the equation (1) to calculate the magnitude of current.  8  ×      10          22           J      /    T  =  I  (  1.274  ×      10          14               m    2    )    I  =  6.3  ×      10    8       A

Alissa Hutchinson · Accepted Answer

b)Yes, at a far distance from the loop, the loop behaves as a dipole. So, the magnetic field due to the loop and earth produces a dipole field. Therefore, they cancel out each other.

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