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Magnetism And Matter

Question
CBSEENPH12039993

A vibration magnetometer placed in magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of 2s in earth's horizontal magnetic field of 24 μT. When a horizontal field of 18 μT is produced opposite to the earth's field by placing a current-carrying wire, the new time period of magnet will be

  • 1s

  • 2s

  • 3s

  • 4s

Solution

B.

2s

Time period in vibration magnetometer
space straight T space equals space 2 straight pi space square root of fraction numerator straight I over denominator straight M space straight x space straight B subscript straight H end fraction end root

straight T proportional to space fraction numerator 1 over denominator square root of straight B subscript straight H end root end fraction
straight T subscript 1 over straight T subscript 2 space equals space square root of fraction numerator left parenthesis straight B subscript straight H right parenthesis subscript 2 over denominator left parenthesis straight B subscript straight H right parenthesis subscript 1 end fraction end root

2 over straight T subscript 2 space equals space square root of 18 over 24 end root

straight T space equals space 2.3 space straight s space equals space 2 space straight s