Question

Find the magnetic field at point p for each of the steady current configurations

Answer 1

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Answer 2

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The total magnetic field at P is the vector sum of the magnetic fields produced by the four segments of the current loop. Along the two straight sections of the loop, and are parallel or opposite, and thus . Therefore, the magnetic field produced by these two straight segments is equal to zero. Along the two circular segments and are perpendicular. Using the right-hand rule it is easy to show that

and where is pointing out of the paper. The total magnetic field at P is therefore equal to the magnetic field at P produced by the circular segment of the current loop is equal to

where is pointing out of the paper. The magnetic field produced at P by each of the two linear segments will also be directed along the negative z axis. The magnitude of the magnetic field produced by each linear segment is just half of the field produced by an infinitely long straight wire .

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