4.13 (a) A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle of 60° with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.

(b) Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)

<p><strong>4.13 </strong>Number of turns of the circular coil, n = 30</p><p>Radius of the coil, r = 8.0 cm = 0.08 m</p><p>Area of the coil, A =<span contenteditable="false"> <math> <mi>π</mi> <msup> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> </span> = <span contenteditable="false"> <math> <mi>π</mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>0.08</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> </span>= 0.0201<span contenteditable="false"> <math> <msup> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> </span></p><p>Current flowing in the coil, I = 6.0 A</p><p>Magnetic field strength, B = 1 T</p><p>Angle between the field line and normal of the coil surface, <span contenteditable="false"> <math> <mi>θ</mi> </math> </span>= 60<strong>°</strong></p><p>The coil experiences a toque in the magnetic field, hence it turns.</p><p>The counter torque is given by the relation, </p><p><span contenteditable="false"> <math> <mi>τ</mi> <mo>=</mo> <mi>n</mi> <mi>I</mi> <mi>B</mi> <mi>A</mi> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>? </mo> <mrow> <mi>θ</mi> </mrow> </mrow> </math> </span>= 30<span contenteditable="false"> <math> <mo>×</mo> <mn>6</mn> <mo>×</mo> <mn>1</mn> <mo>×</mo> <mn>0.0201</mn> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>? </mo> <mrow> <mn>60</mn> <mo>°</mo> </mrow> </mrow> </math> </span> = 3.133 N</p><p>Since the magnitude of the torque is not dependent on the shape of the coil, it depends only on the area. Hence he answer will not change if the circular coil is replaced with a planar coil of same area.</p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment