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Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm,50 turns and carrying currentI  (Ampere) in units of μ0Iπ is :

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Important Questions on Magnetic Effects of Current and Magnetism

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A charged particle carrying charge 1 μC is moving with velocity (2i^+3j^+4k^) m s-1. If an external magnetic field of (5i^+3j^-6k^)×10-3T exists in the region where the particle is moving then the force on the particle is F×10-9 N . the vector F is :
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A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field B. Then the field inside the paramagnetic substance is:

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A galvanometer coil has 500 turns and each turn has an average area of 3×10-4m2. If a torque of 1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5A is flowing through it, the strength of the field (in T) is _________ .
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A small bar magnet is placed with its axis at 30o with an external magnetic field of 0.06 T experiences a torque of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilibrium position is:
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A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B, also bent in the shape of an arc of a circle, carrying a current of 3 A and having radius of 4 cm, are placed as shown in the figure. The ratio of the magnetic fields due to the wires A and B at the common centre O is:

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A circular coil has moment of inertia 0.8 kg m2 around any diameter and is carrying current to produce a magnetic moment of  20 A m2. The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by 60o will be :
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A paramagnetic sample shows a net magnetisation of 6 A m-1 when it is placed in an external magnetic field of 0.4 T at a temperature of 4 K. When the sample is placed in an external magnetic field of 0.3 T at a temperature of 24 K, then the magnetisation will be :
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A galvanometer of resistance G is converted into a voltameter of range 0-1 V by connecting a resistance R in series with it. The additional resistance that should be connected in series with R1 to increase the range of the voltmeter to 0-2V will be :