A bar magnet is oscillating in the Earth's magnetic field with a period T. What happens to this period and motion if this mass is quadrupled:
- Motion remains S.H. with time period = \(\frac T2\)
- Motion remains S.H. with time period = 2T
- Motion remains S.H. with time period = 4T
- Motion remains S.H. with time and period remains nearly constant
The Correct Option is B
Solution and Explanation
Initial mass of the magnet m1 = m and final mass of the magnet m2 = 4 m.
The time period \(T = 2\pi \sqrt {\frac {I}{MB}}\)
\(T = 2\pi \sqrt {\frac {mk^2}{MB}}\)
⇒ \(T ∝ \sqrt {m}\)
Therefore,
\(\frac {T_1}{T_2} = \sqrt {\frac {m_1}{m_2}}\)
\(\frac {T_1}{T_2} = \sqrt {\frac {m}{4m}}\)
\(\frac {T_1}{T_2} = \frac 12\)
\(T_2 = 2T_1\)
\(T_2 = 2T\)
So, the correct option is (B): Motion remains S.H. with time period = 2T
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Concepts Used:
Earth’s Magnetic field
The Earth's magnetic field stretches millions of kilometers into space and resembles a bar magnet. The earth's magnetic pole is positioned between the Northern Pole and the North Pole's Antarctic magnets. That is why a compass magnet's north pole points north (north and south poles attract).
The Earth's magnetic field extends far and wide, but it is very small in terms of field power. It has a field power of merely 40,000 nT as compared to a refrigerator magnet which has a power of 107 nT.
Theory of Earth’s Magnetism
- The Dynamo Effect: The outer core of the earth has molten Iron and other heavy elements in liquid form. The inner core solidifies under the influence of gravity. Therefore, the motion of metallic fluids in the outer core of the earth causes an electric current. Thus, the earth gets its own magnetic field lines.
- Ionization of the Outer Layers: This theory tells us that the rotation of the earth in its own axis produces strong electric current due to the ionization of the outer layers of earth. This produces magnetism due to the movement of the ions. However, the magnetic field will be very weak. The Dynamo Effect is the more acceptable theory.
Components of Earth’s Magnetic Field
These are the components that are responsible for the magnitude and direction of the magnetic field of the earth at a given location:
- Magnetic Declination
- Horizontal Component of Earth’s Magnetic Field
- The angle of Dip or Magnetic Inclination