A long wire $AB$ is placed on a table. Another wire $PQ$ of mass $1.0\, g$ and length $50\, cm$ is set to slide on two rails $PS$ and $QR$. A current of $50\,A$ is passed through the wires. At what distance above $AB$, will the wire $PQ$ be in equilibrium.....$mm$
Medium
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(a) Suppose in equilibrium wire $PQ$ lies at a distance $r$ above the wire $AB$
Hence in equilibrium $mg = Bil$$ \Rightarrow \,\,mg = \frac{{{\mu _0}}}{{4\pi }}\left( {\frac{{2i}}{r}} \right) \times il$
$ \Rightarrow $${10^{ - 3}} \times 10 = {10^{ - 7}} \times \frac{{2 \times {{(50)}^2}}}{r} = 0.5$ $==>$ $r = 25\,mm$
Hence in equilibrium $mg = Bil$$ \Rightarrow \,\,mg = \frac{{{\mu _0}}}{{4\pi }}\left( {\frac{{2i}}{r}} \right) \times il$
$ \Rightarrow $${10^{ - 3}} \times 10 = {10^{ - 7}} \times \frac{{2 \times {{(50)}^2}}}{r} = 0.5$ $==>$ $r = 25\,mm$
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