Correct Answer - Option 4 : length of the suspension
CONCEPT:
Magnet:
-
Magnet is defined as a material that can produce its own magnetic field.
- When a magnet is suspended freely and it gets deflected by a small angle, then due to the earth's horizontal magnetic field its north pole will try to align with the earth's north direction and the south pole will try to align with the earth's south direction.
- So a torque will act on the magnet due to the earth's horizontal magnetic field and the magnet will start oscillating.
EXPLANATION:
- The magnetic dipole moment of the magnet is given as,
\(\Rightarrow M=m\times l\) -----(1)
Where m = pole strength, l = distance between the poles of the magnet
- The torque on the magnet due to the horizontal component of the earth's magnetic field is given as,
\(\Rightarrow \tau=MB_{H}sinθ\) -----(2)
Where θ = angle between M and BH
By equation 1 and equation 2,
\(\Rightarrow \tau=mlB_{H}sinθ\)
If θ is very very small,
\(\Rightarrow sin\theta\approx\theta\)
\(\Rightarrow \tau=mlB_{H}θ\) -----(3)
We know that,
\(\Rightarrow \tau=Iα\) -----(4)
Where I = moment of inertia and α = angular acceleration
By equation 3 and equation 4,
\(\Rightarrow Iα=mlB_{H}θ\)
\(\Rightarrow \frac{\theta}{\alpha}=\frac{I}{mlB_{H}}\) -----(5)
- We know that the time period is given as,
\(\Rightarrow T=2\pi\sqrt{\frac{\theta}{\alpha}}\)
\(\Rightarrow T=2\pi\sqrt{\frac{I}{mlB_{H}}}\) -----(6)
- From equation 6, it is clear that the time period depends on the moment of inertia, pole strength, length of the magnet, and earth's horizontal magnetic field.
- But time period does not depend on the length of the suspension. Hence, option 4 is correct.
