Kelvi

In a uniform magnetic field of $0.049T,$ a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is $9.8 \times 10^{-6}$ kg m $^2.$ If the magnitude of magnetic moment of the needle is $x \times 10^{-5}$ Am $^2,$ then the value of $x$ is:

hard

Magnetism and Matter

2024

physics

$50\pi^2$

$1280\pi^2$

$5\pi^2$

Explanation

To solve this problem, we will use the formula for the time period of oscillation of a magnetic needle in a magnetic field. $\\$ The time period $T$ is given by: $\\ T = 2\pi \sqrt{\frac{I}{MB}} \\$

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