A circular loop of radius 10 cm,500 turns and resistance 2 ohm 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 in 0.25 s. Estimate the magnitude of the emf and current induced in the coil.Horizontal 
component of earth's magnetic  field at the place is 3*10^-5 T.

Asked by Balbir | 26th Jul, 2017, 09:18: PM

Expert Answer:

begin mathsize 12px style Given space that space straight R space equals space 2 space straight capital omega comma space straight theta subscript 1 space equals space 0 space comma space straight theta subscript 2 space equals space 180 degree space
dt space equals space 0.25 space straight s comma space straight B space equals space 3 space cross times space 10 to the power of negative 5 end exponent space space straight T
We space have space to space calculate space straight e space and space straight I.
straight A space equals space πr squared space equals space straight pi space cross times space open parentheses 10 to the power of negative 1 end exponent close parentheses squared space equals space 3.14 space cross times space 10 to the power of negative 2 end exponent space straight m squared
We space know space that space
straight e space equals space minus fraction numerator straight N space open parentheses dϕ close parentheses over denominator dt end fraction space equals space space minus fraction numerator straight N space open parentheses straight ϕ subscript 2 space minus space straight ϕ subscript 1 close parentheses over denominator dt end fraction
rightwards arrow straight e space equals space minus fraction numerator NBA space open parentheses cos space straight theta subscript 1 space space space minus space cos space straight theta subscript 2 close parentheses over denominator dt end fraction space
On space substituting space the space values space and space doing space the space further space calculations comma space we space get
straight e space equals space 3.8 space cross times space 10 to the power of negative 3 end exponent space straight V
To space calculate space straight I comma space we space use
straight I space equals space straight e over straight R space
On space substituting space the space values comma space we space get
straight I space equals space 1.9 space cross times space 10 to the power of negative 3 end exponent space straight A end style

Answered by Yashvanti Jain | 27th Jul, 2017, 11:36: AM