Question:
A long magnet is cut into two equal parts, such that the length of each half is same as that of original magnet. If the period of original magnet is $T$, the period of new magnet is
A long magnet is cut into two equal parts, such that the length of each half is same as that of original magnet. If the period of original magnet is $T$, the period of new magnet is
Updated On: Jun 8, 2024
- $ T $
- $ \frac{T}{2} $
- $ \frac{T}{4} $
- $ 2T $
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The Correct Option is A
Solution and Explanation
Time period $T=2 \pi \sqrt{\frac{I}{M B}}$
As the magnet is cut into two equal parts along axis, then for each part
$I'=\frac{I}{2}$
$M'=\frac{M}{2}$
$\therefore$ Time period of new magnet,
$T'=\sqrt{\frac{I'}{M' B'}}$
$=\sqrt{\frac{I \times 2}{2 \times M \times B}}$
$T'=T$
As the magnet is cut into two equal parts along axis, then for each part
$I'=\frac{I}{2}$
$M'=\frac{M}{2}$
$\therefore$ Time period of new magnet,
$T'=\sqrt{\frac{I'}{M' B'}}$
$=\sqrt{\frac{I \times 2}{2 \times M \times B}}$
$T'=T$
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Concepts Used:
Magnetism & Matter
Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.
Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
Read More: Magnetism and Matter
Some of the properties of the magnetic field lines are:
- The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
- They form closed loops traversing inside the magnet.
- But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
- More number of close lines indicate a stronger magnetic field
- The lines do not intersect each other
- The tangent drawn at the field line gives the direction of the field at that point.