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Three rings, each having equal radius R,...

Three rings, each having equal radius R, are placed mutually perpendicular to each other and each having its centre at the origin of coordinate system. If current I is flowing through each ring, then the magnitude of the magnetic field at the common centre is

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Each ring will produce its magnetic field along its axis. So, the three magnetic field intensities at the common centre due to the rings will be mutually perpendicular. The magnitude of magnetic field intensity at the centre of a circular loop is given by
` B = (mu_(0)i)/(2R)`
Hence, the magnitude of resultant magnetic field at the centre will be `B sqrt3 = (mu_(0)i)/(2R) sqrt3`
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