JEE Main 2023 · Physics · Magnetic Effects of Current · easy

A wire of length 0.2π m is wound into a closely packed circular coil of two turns and carries a current of 5 A. If the magnetic field at the centre…

Numerical answer

A wire of length

0.2\pi\ \mathrm{m}

is wound into a closely packed circular coil of two turns and carries a current of

5\ \mathrm{A}

. If the magnetic field at the centre of the coil is

x\pi\times10^{-6}\ \mathrm{T}

, the value of

x

is (

\mu_0=4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}}

)

Show answer and solution

Answer: 40

Two turns use the whole length:

2\times2\pi r=0.2\pi

, so

r=0.05\ \mathrm m

. Field at the centre of a coil of

N

turns:

B=\dfrac{N\mu_0I}{2r}=\dfrac{2\times4\pi\times10^{-7}\times5}{2\times0.05}=4\pi\times10^{-5}\ \mathrm T=40\pi\times10^{-6}\ \mathrm T

. So

x=40

. (A single turn of radius

0.1\ \mathrm m

would give only

10

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