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A wire is bent in the form of an equila...

A wire is bent in the form of an equilateral triangle PQR of side 10 cm and carries a current of 5.0 A. It is placed in a magnetic field B of magnitude 2.0 T directed perpendicularly to the plane of the loop. Find the forces on the three sides of the triangle.

Text Solution

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Suppose the field and the current have directions as shown in the figure provided.
The force on PQ is `vecF=iveclxxvecB`
or `F_1=5.0Axx10cmxx2.0T=1.0N`
The rule of vector product shows that force `F_1` is perpedicular to PQ and is directed towards the inside of the triangle.
The forces `vecF_2` and `vecF_3` QR and RP can also be obtained similarly. Both the forces are `1.0N` directed perpendicularly to the respective sides and directed inside the triangle.
The three forces `vecF_1, vecF_2` and `vecF_3` will have zero resultant, so that there is no net magnetic force on the triangle. This result can be generalised. Any closed current loop, placed in a homogenous magnetic field, does not experience a net magnetic force.
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