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Question: A magnetic needle has a magnetic moment 5.0 × 10-2 A m2 and moment of inertia 8.5 x 10-7 Kg m2. It p...

A magnetic needle has a magnetic moment 5.0 × 10-2 A m2 and moment of inertia 8.5 x 10-7 Kg m2. It performs oscillation of time period 0.65 s. What is the magnitude of the magnetic field?

A

0.0016 T

B

0.16 T

C

1.6 T

D

16 T.

Answer

0.0016 T

Explanation

Solution

: Here, m=5.0×10−2Am2\mathrm { m } = 5.0 \times 10 ^ { - 2 } \mathrm { Am } ^ { 2 }

T=0.65 s,I=8.5×10−7Kgm2\mathrm { T } = 0.65 \mathrm {~s} , \mathrm { I } = 8.5 \times 10 ^ { - 7 } \mathrm { Kg } \mathrm { m } ^ { 2 }

The magnetic field,

=4×(3.14)2×8.5×10−75×10−2×(0.65)2= \frac { 4 \times ( 3.14 ) ^ { 2 } \times 8.5 \times 10 ^ { - 7 } } { 5 \times 10 ^ { - 2 } \times ( 0.65 ) ^ { 2 } }

=158.69×10−5 T=0.0016 T= 158.69 \times 10 ^ { - 5 } \mathrm {~T} = 0.0016 \mathrm {~T}