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The earth's magnetic field at geomagnetic poles has a magnitude 6.2 xx 10^(-5) T. The radius makes an angleof 135^(@) with the axis of the carth's assumed magnetic dipole. Then, which of the following statement(s) is/are correct? |
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Answer» At a point where `theta = 135^(@)`, magnetic field0 `4.9 xx 10^(-5) T`. The magnetic field B at geomagnetic poles is `B_(p) = (mu_(0))/(4pi)(2M)/R^(3)` The magnetic field due to a dipele at a distance R away from its centre has a magnitude, `B = (mu_(0))/(4pi)M/R^(3)(1+3cos^(2) theta)^(1//2)=1/2B_(p)(1+3cos^(2)theta)^(1//2)` This field is in a direction making an angle `alpha` with the radial direction such that `tanalpha = (tantheta)//2,` as shown in the FIGURE. At a point where `theta = 135^(@)`, the field B is `B = (B_(p))/2(1+3cos^(2)135^(@))^(1//2)` `=1/2xx6.2xx10^(-5) T xx 1.58 = 4.9 xx 10^(-5)T ` The angle `alpha` of this field with the vertical the given by `tan alpha = (tantheta)/2 = (tan 135^(@))/2 = - 0.5` `therefore alpha = 153^(@)` The inclination (dip) is the angle made by the earth.s magnetic field with the horizontal plane. Here it is `153^(@) - 90^(@) = 63^(@)` below the horizontal. 
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