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CBSE Class 12-science Answered

A circular coil of radius 10 cm and resistance 2 Ω is placed with its plane perpendicular to the horizontal component of the earth’s magnetic field. It is rotated about its vertical diameter through 180°. Estimate the charge passed through the coil. Horizontal component of the earth’s magnetic field at the place is 3.0 × 10–5 T. 
Asked by sudesh.sudeshghawri | 01 Mar, 2020, 05:33: PM
answered-by-expert Expert Answer
Figure shows a circular coil is rotated in magnetic field about a vertical axis.
 
 
Induced emf e is given by, e = -dφ/dt  
 
RHS of above equation is  rate of change of magnetic flux
 
begin mathsize 14px style e space equals space minus fraction numerator d over denominator d t end fraction open parentheses B times A close parentheses space equals space minus fraction numerator d over denominator d t end fraction open parentheses B space A space cos theta close parentheses space equals space minus B space A space fraction numerator d space left parenthesis cos theta space right parenthesis over denominator d t end fraction end style ...................(1)
where θ is the angle made by the plane of coil area with rotation axis.
 
Induced current in the coil = induced emf / Resistance = ( e / R )
 
charge dq that is flown in the coil for small rotation time dt  = induced current × time = ( e/ R ) dt  ...................(2)
 
from (1) and (2), we get,  dq = - [ ( B×A)/R ] d(cosθ)
 
total charge q that is flown for half rotation , i.e. from θ=0 to θ=π is given by
 
begin mathsize 14px style q space equals space integral d q space equals space minus integral subscript 1 superscript negative 1 end superscript fraction numerator B cross times A over denominator R end fraction d left parenthesis cos theta right parenthesis space equals space fraction numerator 2 space cross times B space cross times A over denominator R end fraction space equals space fraction numerator 2 cross times 3 space cross times 10 to the power of negative 5 end exponent cross times pi cross times 0.1 cross times 0.1 over denominator 2 end fraction space equals 9.425 space cross times space 10 to the power of negative 7 end exponent C space end style
Answered by Thiyagarajan K | 01 Mar, 2020, 10:39: PM
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