A vibration magnetometer is used at two different places \(\mathrm{A}\) and \(\mathrm{B}\) on the earth. The time period of a magnet suspended freely in the magnetometer at \(\mathrm{A}\) is twice that at \(\mathrm{B}\). If the horizontal component of the earth's magnetic field at \(\mathrm{B}\) is \(32 \times 10^{-6} \mathrm{~T}\), then its value at \(\mathrm{A}\) is

1. A \(\mathrm{H}_{\mathrm{A}}=8 \times 10^{-6} \mathrm{~T}\)
2. B \(\mathrm{H}_{\mathrm{A}}=32 \times 10^{-6} \mathrm{~T}\)
3. C \(\mathrm{H}_{\mathrm{A}}^{\mathrm{A}}=4 \times 10^{-6} \mathrm{~T}\)
4. D \(\mathrm{H}_{\mathrm{A}}=16 \times 10^{-6} \mathrm{~T}\)