A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as SI units) [2024]

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Solution

Q.
A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4 π \times 10^{- 7}$ SI units) [2024]

1 44 mT

2 4.4 T

3 4.4 mT

4 44 T

Ans.
(3)

Number of turns in the coil, $N = 100$

Radius of coil, $r = 10$ $cm = 0.1$ $m$

Current flowing in the coil, $I = 7$ $A$

As, $B = \frac{μ_{0} N I}{2 r}$

$B = \frac{4 π \times 10^{- 7} \times 100 \times 7}{2 \times 0.1} = \frac{4 \times 3.14 \times 10^{- 7} \times 100 \times 7}{2 \times 0.1}$

$= 43.96 \times 10^{- 4} = 4.4$ $mT$

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