Question

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)

Answer 1

The wire lies horizontal will not give any field as it lies along the point.

And the vertical wire will contribute to field.

It is near one end of wire and other end is going infinite.

So field will be half of field to that of long wire in the middle at point d away from it.

Field by long wire in middle at point d away from it is,

B *2πd= u0*I, (by Ampere's law )

So B =(u0*I)/2πd

Here d is 'a' in the given problem

And field wil half as it is towards one end of wire.

So finally B for the system is B= 0.5(u0*I)/2πa

Or B = (u0*I)/4πa