Question
2. When any coil is placed in a uniform mag. field torque is acting on it. The graph of $\tau \rightarrow \theta$ is
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We have a coil placed in a uniform magnetic field. The magnetic field is represented by the vector B. Show more…
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A length $L$ of wire carries a current $i$. Show that if the wire is formed into a circular coil, then the maximum torque in a given magnetic field is developed when the coil has one turn only, and that maximum torque has the magnitude $\tau=L^{2} i B / 4 \pi$.
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Magnetic Force on a Current Carrying Conductor
$$ \begin{array}{l}{\text { (II) A } 15 \text { -loop circular coil } 22 \mathrm{cm} \text { in diameter lies in the } x y} \\ {\text { plane. The current in each loop of the coil is } 7.6 \mathrm{A} \text { clockwise, }} \\ {\text { and an external magnetic field } \vec{\mathbf{B}}=(0.5 \hat{\mathbf{i}}+0.60 \hat{\mathbf{j}}-0.65 \hat{\mathbf{j}}) \mathrm{T}} \\ {\text { passes through the coil. Determine }(a) \text { the magnetic }}\end{array} $$ $$ \begin{array}{l}{\text { moment of the coil, } \vec{\boldsymbol{\mu}} ;(b) \text { the torque on the coil due to the }} \\ {\text { external magnetic field; }(c) \text { the potential energy } U \text { of the }} \\ {\text { coil in the field (take the same zero for } U \text { as we did in our }} \\ {\text { discussion of Fig. } 22}\end{array} $$
A certain fixed length $L$ of wire carries a current $I$ (a) Show that if the wire is formed into a square coil, then the maximum torque in a given magnetic field $B$ is developed when the coil has just one turn. (b) Show that the magnitude of this torque is $\tau=\frac{1}{16} L^{2} I B$
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