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Question
Solve the following problem.
Two small and similar bar magnets have a magnetic dipole moment of 1.0 Am2 each. They are kept in a plane in such a way that their axes are perpendicular to each other. A line drawn through the axis of one magnet passes through the center of other magnet. If the distance between their centers is 2 m, find the magnitude of the magnetic field at the midpoint of the line joining their centers.
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Solution
Let P be the midpoint of the line joining the centres of two bar magnets. As shown in figure, P is at the axis of one bar magnet and at the equator of another bar magnet. Thus, the magnetic field on the axis of the first bar magnet at distance of 1 m from the centre will be,
Ba = `μ_0/(4π)(2"m")/"r"^3`
= `10^-7xx(2xx1.0)/(1)^3`
= 2 × 10−7 Wb/m2
Magnetic field on the equator of second bar magnet will be,
Beq = `μ_0/(4π)("m")/"r"^3`
= `10^-7xx1.0/(1)^3`
= 1 × 10−7 Wb/m2
The net magnetic field at P,
Bnet = `sqrt("B"_"a"^2+"B"_"eq"^2)`
= `sqrt((2xx10^-7)^2+(1xx10^-7)^2)`
= `sqrt((10^-7)^2xx(4+1))`
= `sqrt(5)xx10^-7` Wb/m2
Magnitude of net magnetic field at midpoint of line will be `sqrt(5)xx10^-7` Wb/m2.
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