Magnetic Field Due To A Current Element Biot Savart Law
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Three rings, each with equal radius , are placed mutually perpendicular to each other and each having centre at the origin of the coordinate system. If is the current passing through each ring, the magnetic field value at the common centre is:
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Official Solution
Correct Option: (3)
To determine the magnetic field at the center of three mutually perpendicular rings, each with radius and carrying a current , we use the Biot-Savart Law. The Biot-Savart Law provides the magnetic field contribution from an element of current-carrying wire:
For a complete circular ring, the magnetic field at the center due to symmetry is perpendicular to the plane of the ring, and its magnitude is given by:
Since there are three rings, each mutually perpendicular, the total magnetic field must consider vector addition. Each ring contributes a magnetic field of magnitude:
The net magnetic field is the vector sum:
This results in:
Therefore, the magnetic field at the common center is:
