A long solenoid has 200 turns/cm and carries a current i. The magnetic field at its centre is 6.28 x 10^-2 Wb / m². Another long solenoid has 100 turns/cm and carries a current i / 3. The value of magnetic field at its centre is

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1.05 x10^-3 Wb/m²

1.05 x10^-5 Wb/m²

1.05 x 10^-2 Wb/m²

1.05 x 10^-4 Wb/m²

answer is A.

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Detailed Solution

Magnetic field due to a long solenoid is given by
$B = μ_{0} ni$
$∴ 6 \cdot 28 \times 10^{- 2} = μ_{0} \times (200 \times 10^{2}) \times i$ ……………..(1)
and $B = μ_{0} \times (100 \times 10^{2}) \times (i / 3)$ ………………………(2
Solving eqs. [1) and (2), we get
$B = 1 \cdot 05 \times 10^{- 2} Wb / m^{2}$