A thin ring of radius R metre has charge q column uniformly spread on it. The ring rotates about its axis with a constant frequency of  f revolution/s. The value of magnetic induction in Wb m-2 at the centre of the ring is

  • μoq f/ 2π R

  • μoq / f 2π R

  • μoq / 2 f R

  • μoq / 2 f R


D.

μoq / 2 f R

The magentic field at the centre of the circle

fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction space straight x space fraction numerator 2 πi over denominator straight R end fraction space equals space straight mu subscript straight o over 2 fraction numerator left parenthesis straight q right parenthesis over denominator Rt end fraction

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Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moments m. Which configuration has highest net magnetic dipole moment? 


C.

The direction of magnetic moment is from S to N

mnet
Net magnetic moment will be maximum if cosθ is maximum.
cosθ will be maximum when θ will be minimum. So, at θ = 30° mnet will be maximum.

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Two identical long conducting wire AOB and COD are placed at right angle to each other, with one above other such that O is their common point for the two. The wires carry I1 and I2 currents, respectively. point P is lying at distance d from O along a direction perpendicular to the plane containing the wires. The magnetic field at the point P will be,

  • fraction numerator straight mu subscript straight o over denominator 2 πd end fraction open parentheses I subscript 1 over I subscript 2 close parentheses
  • fraction numerator straight mu subscript straight o over denominator 2 πd end fraction left parenthesis I subscript 1 space plus space I subscript 2 right parenthesis
  • fraction numerator straight mu subscript straight o over denominator 2 πd end fraction space left parenthesis I subscript 1 squared space minus space I subscript 2 squared right parenthesis
  • fraction numerator straight mu subscript straight o over denominator 2 πd end fraction space left parenthesis I subscript 1 squared space minus space I subscript 2 squared right parenthesis

D.

fraction numerator straight mu subscript straight o over denominator 2 πd end fraction space left parenthesis I subscript 1 squared space minus space I subscript 2 squared right parenthesis
The point P is lying at a distance d along the z-axis.



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There are four light -weight rod samples A, B, C D separately suspended by threads. A bar magnet is slowly brought near each sample and the following observations are noted
(i)  A is feebly repelled
(ii) B is feebly attracted
(iii) C is strongly attracted
(iv) D remains unaffected

  • C is a diamagnetic material

  • D is of a ferromagnetic material

  • A is of a non- magnetic material

  • A is of a non- magnetic material


D.

A is of a non- magnetic material

Paramagnetic materials will be feebly attracted, the magnetic material will be feebly repelled and ferromagnetic material will be strongly attracted.

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A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in figure, The new magnetic dipole moment will be

  • M

  • 3M/π

  • 2M/π

  • 2M/π


B.

3M/π

The magnetic moment, M=ml
From figure 
straight I equals straight pi over 3 space straight x space straight r
straight r equals space fraction numerator 3 straight l over denominator straight pi end fraction
therefore comma
New space magnetic space moment
straight M apostrophe space equals space mxr
equals space mx fraction numerator 3 straight l over denominator straight pi end fraction space equals space 3 over straight pi. ml space equals space fraction numerator 3 straight M over denominator straight pi end fraction

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