Two indentical magnetic dipoles of magnetic moment
Question:

Two indentical magnetic dipoles of magnetic moment 1.0Am21.0 \,Am^2 each, placed at a separation of 2m2 \,m with their axes perpendicular to each other. The resultant magnetic field at a point midway between the dipoles is

Updated On: Apr 22, 2024
  • 5×107T\sqrt{5}\times10^{-7}T
  • 5×107T5\times 10^{-7} T
  • 107T10^{-7} T
  • 2×107T2 \times 10^{-7} T
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The Correct Option is A

Solution and Explanation

As the axes are perpendicular, mid point lies on axial line of one magnet and on equitorial line of other magnet
B1=μ04π2Md3\therefore B_{1} =\frac{\mu_{0}}{4 \pi} \frac{2 M}{d^{3}}
=107×2×113=\frac{10^{-7} \times 2 \times 1}{1^{3}}
=2×107T=2 \times 10^{-7} T
and B2=μ04πMd3B_{2} =\frac{\mu_{0}}{4 \pi} \frac{M}{d^{3}}
=107×113=\frac{10^{-7} \times 1}{1^{3}}
=107T=10^{-7} T
As B1B2B_{1} \perp B_{2}
\therefore Resultant magnetic field
=B12+B22=5×107T=\sqrt{B_{1}^{2}}+B_{2}^{2}=\sqrt{5} \times 10^{-7} T
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Concepts Used:

Moving Charges and Magnetism

Moving charges generate an electric field and the rate of flow of charge is known as current. This is the basic concept in Electrostatics. Another important concept related to moving electric charges is the magnetic effect of current. Magnetism is caused by the current.

Magnetism:

  • The relationship between a Moving Charge and Magnetism is that Magnetism is produced by the movement of charges.
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Magnetic Field:

Region in space around a magnet where the Magnet has its Magnetic effect is called the Magnetic field of the Magnet. Let us suppose that there is a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them can be written as,

F = q [ E (r) + v × B (r)] ≡ EElectric +Fmagnetic 

This force was based on the extensive experiments of Ampere and others. It is called the Lorentz force.