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    3.

    Two identical short bar magnets, each having magnetic moment MM, are placed a distance of 2d2d apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is

    A

    μ04π(2)Md3\frac{{{\mu _0}}}{{4\pi }}\left( {\sqrt 2 } \right)\frac{M}{{{d^3}}}

    B

    μ04π(3)Md3\frac{{{\mu _0}}}{{4\pi }}\left( {\sqrt 3 } \right)\frac{M}{{{d^3}}}

    C

    (2μ0π)Md3\left( {\frac{{2{\mu _0}}}{\pi }} \right)\frac{M}{{{d^3}}}

    D

    μ04π(5)Md3\frac{{{\mu _0}}}{{4\pi }}\left( {\sqrt 5 } \right)\frac{M}{{{d^3}}}

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    5.

    Breaking a bar magnet in half results in:

    A

    One magnet with only a north pole and another with only a south pole.

    B

    Two smaller bar magnets, each with a north and south pole.

    C

    Two pieces of non-magnetic material.

    D

    One smaller bar magnet and one piece of non-magnetic material.

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    6.

    Two identical short bar magnets, each having magnetic moment MM, are placed a distance of 2d2d apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is

    A

    μ04π(2)Md3\frac{{{\mu _0}}}{{4\pi }}\left( {\sqrt 2 } \right)\frac{M}{{{d^3}}}

    B

    μ04π(3)Md3\frac{{{\mu _0}}}{{4\pi }}\left( {\sqrt 3 } \right)\frac{M}{{{d^3}}}

    C

    (2μ0π)Md3\left( {\frac{{2{\mu _0}}}{\pi }} \right)\frac{M}{{{d^3}}}

    D

    μ04π(5)Md3\frac{{{\mu _0}}}{{4\pi }}\left( {\sqrt 5 } \right)\frac{M}{{{d^3}}}

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