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In order to measure the magnetic field of the electromagnets, the system makes use of a small magnetic needle to test the magnetic field(B). The needle oscillates around a fixed point in a plane in the direction of B. The period of small oscillations of the needle is-:

Question

In order to measure the magnetic field of the electromagnets, the system makes use of a small magnetic needle to test the magnetic field(B). The needle oscillates around a fixed point in a plane in the direction of B. The period of small oscillations of the needle is-:

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Solution

The period of small oscillations of the needle in a magnetic field can be determined using the formula for the period of a simple harmonic oscillator.

Step 1: Identify the variables The magnetic field strength (B), the moment of inertia of the needle (I), and the magnetic moment of the needle (m) are the key variables in this scenario.

Step 2: Apply the formula The formula for the period (T) of a simple harmonic oscillator is given by T = 2π√(I/mB).

Step 3: Substitute the values Substitute the values of I, m, and B into the formula to find the period of oscillation.

Please note that this formula assumes that the oscillations are small, which allows us to treat the system as a simple harmonic oscillator. For larger oscillations, the period could be different.

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