plz two circular coils X and Y having radii R and R/2 respectively are placed in horizontal - Physics - Moving Charges And Magnetism

Question

plz two circular coils X and Y having radii R and R/2
respectively are placed in horizontal plane with their centres
coinciding with each other coil X has a current I flowing through
it in the clockwise sense what must be the current in coil Y to
make the total magnetic field at the common centre of the two coils
zero ? With the same currents flowing in the two coils ,if the coil
Y is now lifted vertically upwards through a distance R what would
be the net magnetic field at the centre of coil Y?

Vijay Yadav · Accepted Answer

Case 1 BX = BY $[Megnetic field due to current carrying circular coil (at center) B = \frac{μ_{0} I}{2 R}]$ $\Rightarrow \frac{μ_{0} I}{2 R} = \frac{μ_{0} I'}{2 (\frac{R}{2})} \Rightarrow I'= \frac{I}{2}$ Case 2 Magnetic field due to ring Y at the center $B_{Y} = \frac{μ_{0} I}{2 (\frac{R}{2})} = \frac{μ_{0} I}{R}$ (upward) Magnetic field due ring X at the axis at distance R from the center $B_{X} = \frac{μ_{0} {I R}^{2}}{2 (R^{2} + R^{2})^{\frac{3}{2}}} (Downword) = \frac{μ_{0} I R^{2}}{2 (2 R^{2})^{\frac{3}{2}}} = \frac{μ_{0} I}{4 \sqrt{2} R} (Downword)$ Net field at that point BN = BY â€“ BX $= \frac{μ_{0} I}{R} (1 - \frac{1}{4 \sqrt{2}}) [Upword]$