A magnetic needle has magnetic moment 5.8 × 10-2 A m2 and moment of inertia of 7.8 × 10-6 kg m2, it performs 12 complete oscillations in 6.0 s. What is the magnitude of magnetic field?

Question

A magnetic needle has magnetic moment 5.8 × 10-2 A m2 and moment of inertia of 7.8 × 10-6 kg m2, it performs 12 complete oscillations in 6.0 s. What is the magnitude of magnetic field? (A) 0.011 T (B) 0.021 T (C) 0.031 T (D) 0.041 T

Tardigrade Admin · Accepted Answer

Given that,
Magnetic moment of a magnetic needle,

m = 5.8 \times 1 0^{- 2} m^{2}

Moment of inertia of magnetic needle,

I = 7.8 \times 1 0^{- 6} k g m^{2}

Time period of oscillations,

T = \frac{6}{12} = 0.5 s^{- 1}

From

T = 2 π \frac{I}{m B}

we get,
Magnetic field,

B = \frac{4 π ^{2} I}{m T ^{2}} = \frac{4 \times ( 3.14 ) ^{2} \times 7.8 \times 1 0 ^{- 6}}{5.8 \times 1 0 ^{- 2} \times ( 0.5 ) ^{2}} = 0.021 T

Q. A magnetic needle has magnetic moment $5.8 \times 1 0^{- 2} A m^{2}$ and moment of inertia of $7.8 \times 1 0^{- 6} k g m^{2}$ , it performs $12$ complete oscillations in $6.0 s$ . What is the magnitude of magnetic field?

$0.011 T$

$0.021 T$

$0.031 T$

$0.041 T$

Q. A magnetic needle has magnetic moment 5.8×10−2Am2 and moment of inertia of 7.8×10−6kgm2, it performs 12 complete oscillations in 6.0s. What is the magnitude of magnetic field?

0.011T

0.021T

0.031T

0.041T

Given that, Magnetic moment of a magnetic needle, m=5.8×10−2m2 Moment of inertia of magnetic needle, I=7.8×10−6kgm2 Time period of oscillations, T=126​=0.5s−1 From T=2πmBI​​ we get, Magnetic field, B=mT24π2I​=5.8×10−2×(0.5)24×(3.14)2×7.8×10−6​=0.021T

Q. A magnetic needle has magnetic moment $5.8 \times 1 0^{- 2} A m^{2}$ and moment of inertia of $7.8 \times 1 0^{- 6} k g m^{2}$ , it performs $12$ complete oscillations in $6.0 s$ . What is the magnitude of magnetic field?

$0.011 T$

$0.021 T$

$0.031 T$

$0.041 T$