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Find the magnetic induction at point O, if the current carrying wire is in the shape shown in the figure.

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Important Questions on Magnetic Effects of Electric Current

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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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HARD
A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period T. The mass of the loop is m then:
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The magnetic field at the centre of a circular coil of 50 turns and radius 10cm carrying a current of 1A, in tesla is
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The magnetic field at the centre O of the current-carrying square loop shown in the figure is

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The magnitude of a magnetic field at the centre of a circular coil of radius R , having N turns and carrying a current I can be doubled by changing
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Two circular loops L1 and L2 of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop L1 is R1 and that of L2 is R2. The distance between the centres of the loops is 3R1. The magnetic field at the centre of L2 shall be zero if
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An arrangements with a pair of quarter circular coils of radii r and R with a common centre C and carrying a current I is shown.

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The permeability of free space is μ0. The magnetic field at C is

HARD
Two identical wires A and B, each of length l, carry the same current I . Wire A is bent into a circle of radius R and wire B is bent to form a square of side a. If BA and BB are the values of magnetic field at the centres of the circle and square respectively, then the ratio BABB is
MEDIUM
The coefficient of self-induction of a closely wound coil of 100 turns and area of cross-section 1 cm2 is 1 mH. Find the magnetic induction at the centre of its core when a current of 2 A flows in it.
EASY
A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be
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Figure below shows three circuits consisting of concentric circular arcs and straight radial lines. The center of the circle is shown by the dot. Same current flows through each of the circuits. If B1, B2, B3 are the magnitudes of the magnetic field at the center. Which of the following is true?

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Let B1 is the magnetic field at the centre of the current carrying coil of radius R and B2 is the magnetic field on the axis of same circular coil at the distance of 3R. Then the ratio B1B2 is
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Magnetic field at the centre of a circular loop of area A is B. The magnetic moment of the loop will be (μ0= permeability of free space)
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A circular coil of radius R carries an electric current I. The magnetic field due to the coil at a point on the axis of the coil located at a distance r from the centre of the coil, such that rR, the magnetic field at that point is proportional to
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A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of 40π rad s-1 about its axis, perpendicular to its plane. Is the magnetic field its centre is 3.8×10-9 T , then the charge carried by the ring is close to μ0=4π×10-7 N A-2.
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Two infinitely long wires each carrying current I along the same direction are made into the geometry as shown in the figure below.
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The magnetic field at the point P is
EASY
An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the center has magnitude: