A closely wounded circular coil of radius 5 cm produces a magnetic field of $37.68 \times 10^{-4}\,\text{T}$ at its center. The current through the coil is ______ A. [Given, number of turns in the coil is 100 and $\pi=3.14$]

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Magnetic Effects of Current

A closely wounded circular coil of radius 5 cm produces a magnetic field of

37.68 \times 1 0^{- 4} T

at its center. The current through the coil is ______ A.
[Given, number of turns in the coil is 100 and

π = 3.14

]

Answer: 3

Solution

The magnetic field at the center of a circular coil is given by

B = \frac{N μ _{0} I}{2 R}

. Substituting the given values:

37.68 \times 1 0^{- 4} = \frac{100 \times 4 π \times 1 0 ^{- 7} \times I}{2 \times 5 \times 1 0 ^{- 2}}

. Solving for

I

I = \frac{37.68 \times 1 0 ^{- 4} \times 2 \times 5 \times 1 0 ^{- 2}}{100 \times 4 \times 3.14 \times 1 0 ^{- 7}} = 3 A

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Integer answer

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