5.11 At a certain location in Africa, a compass points 12° west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points 60° above the horizontal. The horizontal component of the earth’s field is measured to be 0.16 G. Specify the direction and magnitude of the earth’s field at the location.

<p><strong>5.11 </strong>Given:</p><p>The angle of declination, <span contenteditable="false"> <math> <mi>θ</mi> </math> </span>= 12<span contenteditable="false"> <math> <mo>°</mo> </math> </span></p><p>The angle of dip, <span contenteditable="false"> <math> <mi>β</mi> </math> </span>= 60<span contenteditable="false"> <math> <mo>°</mo> </math> </span></p><p>Horizontal component of Earth’s magnetic field,<span contenteditable="false"> <math> <msub> <mrow> <mrow> <mi>B</mi> </mrow> </mrow> <mrow> <mrow> <mi>H</mi> </mrow> </mrow> </msub> </math> </span> = 0.16 G</p><p>If Earth’s magnetic field be B, we can relate B and <span contenteditable="false"> <math> <msub> <mrow> <mrow> <mi>B</mi> </mrow> </mrow> <mrow> <mrow> <mi>H</mi> </mrow> </mrow> </msub> </math> </span>as <span contenteditable="false"> <math> <msub> <mrow> <mrow> <mi>B</mi> </mrow> </mrow> <mrow> <mrow> <mi>H</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>B</mi> <mrow> <mrow> <mi mathvariant="normal">cos</mi> </mrow> <mo>?</mo> <mrow> <mi>β</mi> </mrow> </mrow> </math> </span></p><p>B = <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>B</mi> </mrow> </mrow> <mrow> <mrow> <mi>H</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mrow> <mrow> <mi mathvariant="normal">cos</mi> </mrow> <mo>?</mo> <mrow> <mi>β</mi> </mrow> </mrow> </mrow> </mrow> </mfrac> </math> </span>=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>0.16</mn> </mrow> </mrow> <mrow> <mrow> <mrow> <mrow> <mi mathvariant="normal">cos</mi> </mrow> <mo>?</mo> <mrow> <mn>60</mn> <mo>°</mo> </mrow> </mrow> </mrow> </mrow> </mfrac> </math> </span> = 0.32 G</p><p>Therefore, the Earth’s magnetic field lies in the vertical plane, 12west of the geographic meridian, making an angle of 60<span contenteditable="false"> <math> <mo>°</mo> <mi> </mi> </math> </span> (upward) with the horizontal direction. Its magnitude is 0.32 G.</p>

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