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Magnetic field strength due to a short bar magnet on its axial line at a distance x is B. What is its value at the same distance on the equatorial line?
  • a)
    B/2
  • b)
    B
  • c)
    2B
  • d)
    4B
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Magnetic field strength due to a short bar magnet on its axial line at...
The magnetic field at any axial point is given by, B =  2μo/ 4πx3
Similarly, the field at any equatorial point is given by, B = μo/ 4πx3
Thus, the field at any equatorial point is half of what it is at an axial point.
 
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Magnetic field strength due to a short bar magnet on its axial line at...
Explanation:
The magnetic field strength due to a short bar magnet on its axial line at a distance x is given by the formula:

B = (μ0/4π) * (2M/x^3)

where μ0 is the permeability of free space, M is the magnetic moment of the bar magnet and x is the distance from the center of the magnet.

On the axial line, x is the distance from the center of the magnet to the point where the magnetic field strength is to be calculated. On the equatorial line, x is the distance from the center of the magnet to the point where the magnetic field strength is to be calculated, but it is perpendicular to the axis of the magnet.

Magnetic Field Strength on the Equatorial Line:
To calculate the magnetic field strength on the equatorial line, we can use the formula:

B = (μ0/4π) * (M/x^3)

where x is the distance from the center of the magnet to the point where the magnetic field strength is to be calculated, and M is the magnetic moment of the bar magnet.

Comparing the two formulas, we can see that the magnetic field strength on the equatorial line is half of the magnetic field strength on the axial line at the same distance. Therefore, the correct option is A, i.e., B/2.

Conclusion:
The magnetic field strength due to a short bar magnet on its axial line at a distance x is B. When the same distance is measured on the equatorial line, the magnetic field strength is half of the magnetic field strength on the axial line at the same distance.
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Read the following text and answer the following questions on the basis of the same:Super magnet The term super magnet is a broad term and encompasses several families of rare-earth magnets that include seventeen elements in the periodic table; namely scandium, yttrium, and the fifteen lanthanides. These elements can be magnetized, but have Curie temperatures below room temperature. This means that in their pure form, their magnetism only appears at low temperatures. However, when they form compounds with transition metals such as iron, nickel, cobalt, etc. Curie temperature rises well above room temperature and they can be used effectively at higher temperatures as well. The main advantage they have over conventional magnets is that their greater strength allows for smaller, lighter magnets to be used. Super magnets are of two categories: (i) Neodymium magnet: These are made from an alloy of neodymium, iron, and boron. This material is currently the strongest known type of permanent magnet. It is typically used in the construction of head actuators in computer hard drives and has many electronic applications, such as electric motors, appliances, and magnetic resonance imaging (MRI). (ii) Samarium-cobalt magnet: These are made from an alloy of samarium and cobalt. This second strongest type of rare Earth magnet is also used in electronic motors, turbo-machinery, and because of its high temperature range tolerance may also have many applications for space travel, such as cryogenics and heat resistant machinery. Rare-earth magnets are extremely brittle and also vulnerable to corrosion, so they are usually plated or coated to protect them from breaking, chipping, or crumbling into powder. Since super magnets are about 10 times stronger than ordinary magnets, safe distance should be maintained otherwise these may damage mechanical watch, CRT monitor, pacemaker, credit cards, magnetically stored media etc. These types of magnets are hazardous for health also. The greater force exerted by rare-earth magnets creates hazards that are not seen with other types of magnet. Magnets larger than a few centimeters are strong enough to cause injuries to body parts pinched between two magnets or a magnet and a metal surface, even causing broken bones. Neodymium permanent magnets lose their magnetism 5% every 100 years. So, in the truest sense Neodymium magnets may be considered as a permanent magnet.Super magnets are about _____ time stronger than ordinary magnets.

Read the following text and answer the following questions on the basis of the same:Super magnetThe term super magnet is a broad term and encompasses several families of rare-earth magnets that include seventeen elements in the periodic table; namely scandium, yttrium, and the fifteen lanthanides. These elements can be magnetized, but have Curie temperatures below room temperature. This means that in their pure form, their magnetism only appears at low temperatures. However, when they form compounds with transition metals such as iron, nickel, cobalt, etc. Curie temperature rises well above room temperature and they can be used effectively at higher temperatures as well. The main advantage they have over conventional magnets is that their greater strength allows for smaller, lighter magnets to be used. Super magnets are of two categories: (i) N eodymium magnet: These are made from an alloy of neodymium, iron, and boron. This material is currently the strongest known type of permanent magnet. It is typically used in the construction of head actuators in computer hard drives and has many electronic applications, such as electric motors, appliances, and magnetic resonance imaging (MRI). (ii) Samarium-cobalt magnet: These are made from an alloy of samarium and cobalt. This second strongest type of rare Earth magnet is also used in electronic motors, turbo-machinery, and because of its high temperature range tolerance may also have many applications for space travel, such as cryogenics and heat resistant machinery. Rare-earth magnets are extremely brittle and also vulnerable to corrosion, so they are usually plated or coated to protect them from breaking, chipping, or crumbling into powder. Since super magnets are about 10 times stronger than ordinary magnets, safe distance should be maintained otherwise these may damage mechanical watch, CRT monitor, pacemaker, credit cards, magnetically stored media etc.These types of magnets are hazardous for health also. The greater force exerted by rare-earth magnets creates hazards that are not seen with other types of magnet. Magnets larger than a few centimeters are strong enough to cause injuries to body parts pinched between two magnets or a magnet and a metal surface, even causing broken bones. Neodymium permanent magnets lose their magnetism 5% every 100 years. So, in the truest sense Neodymium magnets may be considered as a permanent magnet.Curie point of pure rare Earth elements is

Magnetic field strength due to a short bar magnet on its axial line at a distance x is B. What is its value at the same distance on the equatorial line?a)B/2b)Bc)2Bd)4BCorrect answer is option 'A'. Can you explain this answer?
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