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Question
A hypothetical magnetic field existing in a region is given by `vecB = B_0 vece` where `vece`_r denotes the unit vector along the radial direction. A circular loop of radius a, carrying a current i, is placed with its plane parallel to the x−y plane and the centre at (0, 0, d). Find the magnitude of the magnetic force acting on the loop.
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Solution
Given:
A hypothetical magnetic field existing in a region, `vecB = B_0 vece_r` where denotes the unit vector along the radial direction.
A circular loop of radius a
So, the length of the loop, l = 2πa
Electric current through loop = i
As per the question, the loop is placed with its plane parallel to the X−Y plane and its centre is at (0, 0, d).
Here, angle between the length of the loop and the magnetic field is θ. Magnetic force is given by
`|vecF| = vecilxxvecB`
`vecF = i(2piaxxvecB)`
`vecF = i2piaBsintheta`
=`(i2piaB_0a)/sqrt(a^2 + d^2`
`= (i2piB_0a^2)/sqrt(a^2 + d^2`
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