Question:
Two short magnets have equal pole strengths but one is twice as long as the other. The shorter magnet is placed 20 cm in tan A position from the compass needle. The longer magnet must be placed on the other side of the magnetometer for no deflection at a distance equal to
Two short magnets have equal pole strengths but one is twice as long as the other. The shorter magnet is placed 20 cm in tan A position from the compass needle. The longer magnet must be placed on the other side of the magnetometer for no deflection at a distance equal to
Updated On: May 5, 2024
- $20\,cm$
- $ 20 \times (2)^{1/3}\, cm $
- $ 20 \times (2)^{2/3} \,cm $
- $ 20 \times (2)^{4/3} \,cm $
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The Correct Option is B
Solution and Explanation
In tangent $A$ setting arms of the magnetometer are along east-west ( $ \perp $ to magnetic meridian). Magnet is placed with its length paralleI to the arms.
As, $ F = H \,tan\, \theta $
$ \therefore \frac{\mu_0}{\pi} \times \frac{2M}{d^3} = H\, tan\, \theta $
For no deflection in tan A position
$ \frac{\mu_0}{4 \pi} \frac{2M_1}{d_1^3} = \frac{\mu_0}{4 \pi} \frac{2M_2}{d_2^3} $
$ \therefore \frac{M_1}{M_2} = \bigg(\frac{d_1}{d_2} \bigg)^3$ or $\frac{1}{2} = \bigg(\frac{20}{d_2}\bigg)^3 $
or $d_2 = 20 \times (2)^{1/3}\, cm $
As, $ F = H \,tan\, \theta $
$ \therefore \frac{\mu_0}{\pi} \times \frac{2M}{d^3} = H\, tan\, \theta $
For no deflection in tan A position
$ \frac{\mu_0}{4 \pi} \frac{2M_1}{d_1^3} = \frac{\mu_0}{4 \pi} \frac{2M_2}{d_2^3} $
$ \therefore \frac{M_1}{M_2} = \bigg(\frac{d_1}{d_2} \bigg)^3$ or $\frac{1}{2} = \bigg(\frac{20}{d_2}\bigg)^3 $
or $d_2 = 20 \times (2)^{1/3}\, cm $
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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.