A 100 turn rectangular coil ABCD (in X-Y plane) is hung from one arm of a balance (shown in figure). A mass 500 g is added to the other arm to balance the weight of the coil. A current 4.9 A passes through the coil and a constant magnetic field of 0.2 T acting inward (in x-z plane) is switched on such that only arm CD of length 1 cm lies in the field. How much additional mass m must be added to regain the balance?

<p>This is a Long Answer Type Questions as classified in NCERT Exemplar</p><p><strong>Explanation –&nbsp;</strong>for equilibrium balance net torque should be zero</p><p>Mgl= Wcoil<em>l</em></p><p>500gl = Wcoil<em>l</em></p><p>Wcoil= 500 <span contenteditable="false"> <math> <mo>*</mo> </math> </span>9.8N</p><p>Taking moment of force about mid point then magnetic field</p><p>Mgl+mgl=Wcoil<em>l</em>+IBlsin90</p><p>Mgl=BIL<em>l</em></p><p>M= <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>0.2</mn> <mo>*</mo> <mn>4.9</mn> <mo>*</mo> <mn>1</mn> <mo>*</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mn>9.8</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>10</mn> </math> </span>-3kg= 1g</p>

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