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A uniform conducting wire of length 12a and resistance R is wound up as a current carrying coil in the shape of : (i) an equilateral triangle of side a, (ii) a square of sides a and, (iii) a regular hexagon of sides a. The coil is connected to a voltage source V_(0) . Find the magnetic moment of the coils in each case. |
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Answer» Solution :Magnetic dipole moment for this coil is m = nIA (i) For equilateral triangle : Side of equilateral triangle be a. Total length of wire be 12 a. `therefore` NUMBER of turns of coil N = 3 Magnetic dipole moment for coil, `m=nIA=4I(sqrt3/4a^(2))" "[BECAUSEA=(SQRT3A^(2))/4]` `m=Ia^(2)sqrt3`  (ii) For square coil : Number of turn n = 3, Area of square A = `a^(2)` Magnetic dipole moment for square LOOP = nIA = `3I(a^(2))`  (iii) For hexagon loop : Number of turn n = 2. Magnetic dipole moment, m = nIA = `2I((6sqrt3)/4a^(2))` m = `3sqrt3Ia^(2)` 
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