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4. The wire shown in Fig. below is infinitely long and carries a current I. Calculate the magnitude and direction of the magnetic field that this current produces at point P. (Use Ampere’s law)
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♦ Relevant knowledge
The magnetic field can be described as the electromagnetic field that surrounds the magnet which exerts magnetic force upon the electro-charged particles within the field of magnetic force. It is in a straight line with the electrical field. The unit of measurement that measures the magnetic field can be found Tesla.
As it is horizontal, the wire will not create any field because it is lying along the point.
The vertical wire will also contribute to the field.
It’s near the wire end, and the other end is going infinity.
Field will then be half the field of long wire in its middle at point d from it.
At point d away, field by long wire in the middle
B *2pd= U0*I (according to Ampere’s Law )
So B = (u0*I]/2pd
Here, d is “a” in the given problem
The field will be half the size of what it is towards one end.
Finally, B for the system is now B= 0.5 (u0*I),/2pa
Or B = (u0*I),/4pa