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Magnetism And Matter

Question
CBSEENPH12039809
Wired Faculty App

A wire carrying current I has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to X  -axis while semicircular portion of radius R is lying in a Y-Z plane. The magnetic field at point  O is.

  • bold B space equals space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight l over straight R space left parenthesis straight pi stack space straight i with hat on top space plus 2 straight k with hat on top right parenthesis
  • bold B space equals space minus fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight l over straight R space left parenthesis straight pi stack space straight i with hat on top space minus 2 straight k with hat on top right parenthesis
  • bold B space equals negative space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight l over straight R space left parenthesis straight pi stack space straight i with hat on top space plus 2 straight k with hat on top right parenthesis
  • bold B space equals space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight l over straight R space left parenthesis straight pi stack space straight i with hat on top space minus 2 straight k with hat on top right parenthesis

Solution

C.

bold B space equals negative space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight l over straight R space left parenthesis straight pi stack space straight i with hat on top space plus 2 straight k with hat on top right parenthesis

The magnetic fiedl in the different regions is given by 

bold B subscript bold 1 space equals space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight x straight l over straight R space left parenthesis negative straight k with hat on top right parenthesis bold B subscript bold 3 space equals space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight l over straight R space left parenthesis negative straight k with hat on top right parenthesis bold B subscript bold 2 bold space equals space space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight l over straight R space left parenthesis negative stack space straight i with hat on top space right parenthesis The space net space magnetic space field space at space the space centre space straight O space is space straight B space equals space straight B subscript 1 space plus straight B subscript 2 space end subscript plus straight B subscript 3 space equals space space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight x straight l over straight R space left parenthesis negative straight k with hat on top right parenthesis plus space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight l over straight R space left parenthesis negative straight k with hat on top right parenthesis space plus space space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight l over straight R space left parenthesis negative stack space straight i with hat on top space right parenthesis bold B bold space bold equals bold space bold minus space space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction straight l over straight R space left parenthesis 2 straight k with hat on top plus space straight pi straight i with hat on top space right parenthesis

Some More Questions From Magnetism and Matter Chapter

Answer the following question:
The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past?

Answer the following question:
The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

A bar magnet of magnetic moment 1.5 JT–1 lies aligned with the direction of a uniform magnetic field of 0.22 T.
(a) What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction, (ii) opposite to the field direction?
(b)    What is the torque on the magnet in cases (i) and (ii)?

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