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Moving Charges And Magnetism

Question
CBSEENPH12040010
Wired Faculty App

A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane.  if the current in the loop is i. The resultant magnetic field due to the two semicircular parts at their common centre is

  • fraction numerator straight mu subscript straight o space straight i over denominator 2 square root of 2 straight R end root end fraction
  • fraction numerator straight mu subscript 0 straight i over denominator 2 straight R end fraction
  • fraction numerator straight mu subscript straight o straight i over denominator 4 straight R end fraction
  • fraction numerator straight mu subscript straight o straight i over denominator square root of 2 straight R end fraction

Solution

A.

fraction numerator straight mu subscript straight o space straight i over denominator 2 square root of 2 straight R end root end fraction straight B subscript 1 space equals space straight B subscript 2 space equals space fraction numerator straight mu subscript 0 straight i over denominator 4 straight R end fraction The space magnetic space field space at space their space common space centre bold B with bold rightwards arrow on top bold space bold equals bold space stack bold B subscript bold 1 with bold rightwards arrow on top bold space bold plus bold space stack bold B subscript bold 2 with bold rightwards arrow on top straight B space equals space square root of straight B subscript 1 superscript 2 plus straight B subscript 2 superscript 2 end root space equals square root of open parentheses fraction numerator straight mu subscript straight o straight i over denominator 4 straight R end fraction close parentheses squared plus open parentheses fraction numerator straight mu subscript 0 straight i over denominator 4 straight R end fraction close parentheses squared end root equals space straight B space fraction numerator straight mu subscript 0 straight i over denominator 2 square root of 2 straight R end root end fraction

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M1 and M2 have the following particulars:
R1 = 10 Ω   N1 = 30,
A1 = 3.6 x 10–3 m2,  B1 = 0.25 T
R2 = 14 Ω;  N2 = 42,
A2 = 1.8 x 10–3 m2, B2 = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M2 and M1.

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