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Two short magnets of equal dipole moment...

Two short magnets of equal dipole moments M are fastened perpendicularly at their centres Find the effective magnetic moment.

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To find the effective magnetic moment of two short magnets with equal dipole moments \( M \) that are fastened perpendicularly at their centers, we can follow these steps: ### Step 1: Understanding the Configuration We have two magnetic dipoles, each with a dipole moment \( M \). They are oriented at a right angle (90 degrees) to each other. ### Step 2: Representing the Dipole Moments as Vectors Since magnetic dipole moments are vector quantities, we can represent them as vectors. Let’s denote the first dipole moment as vector \( \vec{M_1} \) and the second dipole moment as vector \( \vec{M_2} \). ...
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Knowledge Check

  • Two short magnets of equal dipole moments M are fastened perpendicularly at their centres as shown in the figure. The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is

    A
    `(mu_0)/(4pi)(M)/(d^3)`
    B
    `(mu_0)/(4 pi) (sqrt(2)M)/(d^3)`
    C
    `(mu_0)/(4 pi)(2sqrt(2)M)/(d^3)`
    D
    `(mu_0)/(4pi)(2M)/(d^3)`

  • Two short bar magnets of equal dipole moments 'M' each are fastened perpendicular at their centers as shown in figure. The magnitude of the magnetic field at 'P' at a distance d from their common centre as shown in figure is

    A
    `(mu_(0))/(4pi)(M)/d^(3)`
    B
    `(mu_(0))/(4pi)(2sqrt2M)/d^(3)`
    C
    `(mu_(0))/(4pi)(2M)/d^(3)`
    D
    `(mu_(0))/(2pi)(M)/d^(3)`

  • Two short bar magnets are taken and fastened together perpendicularly by their centres as shown in figure. Magnetic moment of each magnet is M and A is a point on bisector of this system at a distance d from the centre as N A S shown in figure. Magnetic field intensity at point A is

    A
    `B = (mu_0)/(4pi) (M)/(d^3)`
    B
    `B = (mu_0)/(4pi) (2M)/(d^3)`
    C
    `B = (mu_0)/(4pi) (M sqrt2)/(d^3)`
    D
    `B = (mu_0)/(4pi) (2 sqrt2M)/(d^3)`

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