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Question
A wire, carrying a current i, is kept in the x−y plane along the curve y = A sin `((2x)/lamda x)`. magnetic field B exists in the z direction. Find the magnitude of the magnetic force on the portion of the wire between x = 0 and x = λ.
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Solution
Given:
Electric current flowing through the wire = i
The wire is kept in the x−y plane along the curve, `y = A sin ((2x)/lamda x)`
Magnetic field (B) exists in the z direction.
We have to find the magnetic force on the portion of the wire between x = 0 and x = λ.
Magnetic force is given by
`vecF = i veclxxvecB`
For a small element dl,
`dvecF = i (dl xx vecB)`
The effective force on the whole wire is equivalent to the force on a starlight wire of length λ placed along the x axis.
So,
F = iB \[\int\limits_0^{λ}\] dl
`⇒ F = ilamdaB`
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