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An insulating thin rod of length l has a linear charge density ρx=ρ0xl on it. The rod is rotated about an axis passing through the origin x=0 and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is:

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Important Questions on Magnetic Effects of Current and Magnetism

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JEE Main
IMPORTANT
A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th and Tc respectively, then:
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JEE Main
IMPORTANT
At some location  the horizontal component of earth's magnetic field is 18×10-6 T. At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes 45° angles with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is:
MEDIUM
JEE Main
IMPORTANT
A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45° and 40 times per minute where the dip is 30°. If B1 and B2 are the net magnetic fields due to the earth at the two places respectively, then the ratio B1B2 is approximately equal to
HARD
JEE Main
IMPORTANT
A galvanometer of resistance 100 Ω has 50  divisions on its scale and has sensitivity of 20μA/ division . It is to be converted to voltmeter with three ranges, of 0-2 V,0-10 V and 0-20 V. The appropriate circuit to do so is:
MEDIUM
JEE Main
IMPORTANT
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.
MEDIUM
JEE Main
IMPORTANT
An electron, moving along the x- axis with an initial energy of 100 eV, enters a region of magnetic field B=1.5×10-3 Tk^ at S (see figure). The field extends between x=0 and x=2 cm. The electron is detected at the point Q on a screen placed 8 cm away from the point S. The distance d between P and Q (on the screen) is:
(electron’s charge 1.6×10-19 C , mass of electron =9.1×10-31 kg )
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HARD
JEE Main
IMPORTANT
A moving coil galvanometer, having a resistance G, produces full scale deflection when a current IG flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to IoI0>Ig by connecting a shunt resistance RA to it and (ii) into a voltmeter of range 0 to VV=GI0 by connecting a series resistance RV to it. Then,
MEDIUM
JEE Main
IMPORTANT

Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5 A. (See figure) μ0=4π×10-7 NA-2

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