Question

A single current-carrying circular loop of radius R is placed next to a long, straight wire, as shown in the
figure. The current I in the wire flows to the right and the a current I flows counter-clockwise on the loop. What is the net magnetic field produce at the center of the loop?

I R/2

Answer 1

Magnetic field at the centre of the loop due to the current carrying long straight wire = ×i/(2πr)

here, = permeability of free space

i = current on the wire.

r = distance of the centre from the wire= (R+R/2) = 3R/2.

So, the magnetic field at the centre of the loop due to the long straight wire = (​​​​​×i)/{(2π)×(3R/2)}

=> The magnetic field= (×i)/3πR

The magnetic field at the centre due to the circular loop= (×i)/2R

The net magnetic field= (×i)/3πR + (×i)/2R

=> The net magnetic field= [(×i)/R]×[1/3π + 1/2]

=> The net magnetic field= 0.606(×i)/R .

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