Two concentric thin circular rings of radii 5 | vedclass

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(A) Given: $r_1 = 40 	ext{ cm} = 0.4 	ext{ m}$,$r_2 = 50 	ext{ cm} = 0.5 	ext{ m}$,$I = 3.5 	ext{ A}$.The magnetic field at the centre of a circu

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$11 	imes 10^{-7} 	ext{ T}$

Vedclass · Answer

(A) Given: $r_1 = 40 	ext{ cm} = 0.4 	ext{ m}$,$r_2 = 50 	ext{ cm} = 0.5 	ext{ m}$,$I = 3.5 	ext{ A}$.The magnetic field at the centre of a circular ring is given by $B = \frac{\mu_0 I}{2r}$.Since the currents are in opposite directions,the net magnetic field at the centre is the difference between the fields produced by the two rings:$B_{net} = |B_1 - B_2| = \left| \frac{\mu_0 I}{2r_1} - \frac{\mu_0 I}{2r_2} ight| = \frac{\mu_0 I}{2} \left( \frac{1}{r_1} - \frac{1}{r_2} ight)$.Substituting the values:$B_{net} = \frac{4\pi 	imes 10^{-7} 	imes 3.5}{2} \left( \frac{1}{0.4} - \frac{1}{0.5} ight)$$B_{net} = 2\pi 	imes 10^{-7} 	imes 3.5 	imes (2.5 - 2.0)$$B_{net} = 7\pi 	imes 10^{-7} 	imes 0.5 = 3.5\pi 	imes 10^{-7} 	ext{ T}$.Using $\pi \approx 3.14$,$B_{net} \approx 3.5 	imes 3.14 	imes 10^{-7} \approx 10.99 	imes 10^{-7} 	ext{ T} \approx 11 	imes 10^{-7} 	ext{ T}$.

Two concentric thin circular rings of radii $50 \text{ cm}$ and $40 \text{ cm}$,each carry a current of $3.5 \text{ A}$ in opposite directions. If the two rings are coplanar,the net magnetic field due to the two rings at their centre is

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