An insulated wire is wound so that it forms a flat coil with N = 200 turns. The radius of the innermost turn is

Question

An insulated wire is wound so that it forms a flat coil with N = 200 turns. The radius of the innermost turn is $r_{1} = 3 cm$ , and of the outermost turn $r_{2} = 6 cm$ . If 20 mA current flow in it then the magnetic moment will be $α \times 10^{- 2} A \cdot m^{2}$ . The value of $α$ is ________. [2026]

Smart Achievers · Accepted Answer

(2)

$n = \frac{N}{r_{2} - r_{1}} = \frac{200}{3 \times 10^{- 2}} \frac{turn}{m}$

$d M = n d r I π r^{2}$

$M = \int d M = n I π \int_{r_{1}}^{r_{2}} r^{2} d r$

$M = \frac{200 \times 20 \times 10^{- 3} \times 3.14 \times [216 - 27] \times 10^{- 6}}{3 \times 10^{- 2} \times 3}$

$M = 2.64 \times 10^{- 2} A . m^{2}$

Solution

1 4.4

2 2.64

3 3.25

4 1.2

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