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Moving Charges And Magnetism

Question
CBSEENPH12039842
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Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 2I, respectively. The resultant magnetic field induction at the centre will be

  • fraction numerator square root of 5 straight mu subscript straight o straight I over denominator 2 straight R end fraction
  • fraction numerator 3 straight mu subscript straight o straight I over denominator 2 straight R end fraction
  • fraction numerator straight mu subscript straight o straight I over denominator 2 straight R end fraction
  • fraction numerator straight mu subscript straight o straight I over denominator straight R end fraction

Solution

A.

fraction numerator square root of 5 straight mu subscript straight o straight I over denominator 2 straight R end fraction

The magnetic field (B) at the centre of circular current carrying coil of radius R and current I,
straight B equals space fraction numerator straight mu subscript straight o straight I over denominator 2 straight R end fraction Similarly comma space if space current space equals space 2 straight I comma space then Magnetic space field space equals space fraction numerator straight mu subscript straight o 2 straight I over denominator 2 straight R end fraction space equals space 2 straight B so space resultant space magnetic space field equals space square root of straight B squared space plus left parenthesis 2 straight B right parenthesis squared end root space equals space square root of 5 straight B squared end root space square root of 5 straight B end root space equals space fraction numerator square root of 5 straight mu subscript straight o straight I over denominator 2 straight R 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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