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Two short magnet A and B of magnetic dip...

Two short magnet `A` and `B` of magnetic dipole mement `M_(1)` and `M_(2)` respectively are placed as shown.The axis of `A` and the equatorial line of `B` are the same.Find the magnetic force on one magnet due to other.

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To find the magnetic force on one magnet due to the other, we can follow these steps: ### Step 1: Understand the Configuration We have two short magnets, A and B, with magnetic dipole moments \( M_1 \) and \( M_2 \) respectively. The axis of magnet A coincides with the equatorial line of magnet B. ### Step 2: Magnetic Field at the Equatorial Line The magnetic field \( B \) at the equatorial line of a magnetic dipole can be expressed as: \[ B = \frac{\mu_0}{4\pi} \cdot \frac{2M}{r^3} \] where \( M \) is the magnetic moment of the magnet, \( r \) is the distance from the magnet, and \( \mu_0 \) is the permeability of free space. ### Step 3: Magnetic Field Due to Magnet B at the Location of Magnet A Since we are interested in the magnetic field at the location of magnet A due to magnet B, we can write: \[ B_B = \frac{\mu_0}{4\pi} \cdot \frac{2M_2}{r^3} \] where \( M_2 \) is the magnetic moment of magnet B and \( r \) is the distance between the two magnets. ### Step 4: Force on Magnet A Due to Magnet B The force \( F \) on a magnetic dipole in a magnetic field is given by: \[ F = M \cdot \frac{dB}{dr} \] For magnet A, we need to calculate the derivative of the magnetic field \( B_B \) with respect to \( r \): \[ \frac{dB_B}{dr} = \frac{d}{dr} \left( \frac{\mu_0}{4\pi} \cdot \frac{2M_2}{r^3} \right) = -\frac{3\mu_0}{4\pi} \cdot \frac{2M_2}{r^4} \] ### Step 5: Substitute into the Force Equation Now we can substitute this derivative back into the force equation for magnet A: \[ F_{A} = M_1 \cdot \left(-\frac{3\mu_0}{4\pi} \cdot \frac{2M_2}{r^4}\right) \] This simplifies to: \[ F_{A} = -\frac{3\mu_0}{4\pi} \cdot \frac{2M_1M_2}{r^4} \] ### Step 6: Conclusion The magnetic force on magnet A due to magnet B is: \[ F_{A} = -\frac{3\mu_0}{4\pi} \cdot \frac{2M_1M_2}{r^4} \] This indicates that the force is attractive since it is negative. ---

To find the magnetic force on one magnet due to the other, we can follow these steps: ### Step 1: Understand the Configuration We have two short magnets, A and B, with magnetic dipole moments \( M_1 \) and \( M_2 \) respectively. The axis of magnet A coincides with the equatorial line of magnet B. ### Step 2: Magnetic Field at the Equatorial Line The magnetic field \( B \) at the equatorial line of a magnetic dipole can be expressed as: \[ ...
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  • Two identical magnetic dipoles of magnetic moments 1*0Am^2 each are placed at a separation of 2m with their axes perpendicular to each other. What is the resultant magnetic field at a point midway between the dipoles?

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