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A circular loop of radius 9.7 cm carries a current 2.3 A. Obtain the magnitude of the magnetic field (a) at the centre of the loop (b) at a distance of 9.7 cm from the - Physics

Sum

A circular loop of radius 9.7 cm carries a current 2.3 A. Obtain the magnitude of the magnetic field
(a) at the centre of the loop
(b) at a distance of 9.7 cm from the centre of the loop but on the axis.

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Solution

Data: R = z = 9.7 cm = 9.7 x 10-2 m, I = 2.3 A, N = l

(a) At the centre of the coil:

The magnitude of the magnetic induction,

B = `(mu_0"NI")/(2"R")`

`= ((4pi xx 10^-7)(1)(2.3))/(2(9.7 xx 10^-2)) = (2 xx 3.142 xx 2.3)/9.7 xx 10^-5`

`= 1.49 xx 10^-5` T

(b) On the axis, at a distance z = 02 m from the coil:

B = `mu_0/(4pi) (2pi"IR"^2)/(("R"^2 + "z"^2))^(3/2)`

`("R"^2 + "z"^2)^(3/2) = (2"R"^2)^(3/2) = 2sqrt2"R"^3`     (∵ R = z)

∴ B = `mu_0/(4pi) (2pi"IR"^2)/(2sqrt2"R"^3) = mu_0/(4pi) (pi"I")/(sqrt2"R")`

`= (10^-7) (3.142 xx 2.3)/(1.414 xx 9.7 xx 10^-2)`

`= 7.227/13.72 xx 10^-5 = 5.267 xx 10^-6 "T" = 5.267 mu "T"`

Concept: Magnetic Lines for a Current Loop
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APPEARS IN

Balbharati Physics 12th Standard HSC Maharashtra State Board
Chapter 10 Magnetic Fields due to Electric Current
Exercises | Q 11 | Page 250
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