A long straight wire carries a current I. If the magnetic field at a distance d from the wire has a magnitude B, what is the magnitude of the magnetic field at a distance 2d from the wire

Explanation:

As the field of current wire passing through the loop is same in direction (normally inward) but not uniform in magnitude.

So, we will use integtation method for finding the flux.

The same flux through a thin reactangular strip of length l and with dx, is given by

dϕB=Bx.dS=B(x)dScos180∘.

Magnetic field due to a long straight wire carrying current I is given by B=μ0I2πx, and area, dS=l×dx.

∴ ϕB=∫dϕB=−∫μ02πIlx.dx=−μ02πIl[logex]x=a+lx=a

=−μ02π.Ill

6 cos 34, 6 sin 34 trig

fgravity=10x10=100n case 1

fgravity=30x20=600n case 2

6 times more