4.8 A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.

<p><strong>4.8 </strong>Length of the solenoid, l = 80 cm = 0.8 m</p><p>Total number of turns in 5 layers, n = 5<span contenteditable="false"> <math> <mo>×</mo> <mn>400</mn> </math> </span> = 2000</p><p>Diameter of the solenoid, D = 1.8 cm = 0.018 m</p><p>Current carrying by the solenoid, I = 8.0 A</p><p>Magnitude of the magnetic field inside the solenoid near its centre is given by the relation,</p><p>B =<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mi>N</mi> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mi>l</mi> </mrow> </mrow> </mfrac> </math> </span> , where <span contenteditable="false"> <math> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> </math> </span>= permeability of free space = 4<span contenteditable="false"> <math> <mi>π</mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </mrow> </msup> </math> </span> Tm<span contenteditable="false"> <math> <msup> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> </math> </span></p><p>B = <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>4</mn> <mi>π</mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>2000</mn> <mo>×</mo> <mn>8</mn> </mrow> </mrow> <mrow> <mrow> <mn>0.8</mn> </mrow> </mrow> </mfrac> </math> </span>= 2.51<span contenteditable="false"> <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </math> </span> T</p>

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