A plane loop shown in fig. is ahaped as 2 squares wid sides a = 20 cm and b = 10 cm and is introduced into a uniform magnetic field at right angles to the loops plane. the magnetic induction wid time as B=Bosin t where Bo= 10 mT and = 100s-1. find the amplitude of the current induced in the loop if its resistance per unit lenght is equal to = 50 mohm/m. the inductance of the loops is to be neglected.
i am assuming current to be clockwise in 'a' so it shud be anticlockwise in b ( get it by making arrow of flow of curret in each branch
total resistace of loop is, 50 * ( 4*0.2 + 4*0.1) *10^-3 = 6 * 10^-2 ohm now net flux thru arrangemet'Z' = flux thru a - flux thru b = B ( a^2-b^2) = B* 3*10^-3 so net emf thru loop = dZ/dt = wB(not)coswt * 3* 10^-3
so current in loop = E/r = wB(not)coswt * 3* 10^-3/r
now E max = wB(not) * 3*10^-3=100*10^-3 * 3*10^-3= 3*10^-4 { put coswt=1 , current is also varying here so to find max current we did this.. } I max = 3*10^-4/6*10^-2 = 0.5 * 10^-2 = 5mA
check the calculations ur self otherwise the concept is this only, do ask if u hav doubts:)
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t where Bo= 10 mT and 
= 100s-1.
= 50 mohm/m. the inductance of the loops is to be neglected.![[Thumb - untitled.JPG]](/upload/2007/12/28/e4abe48374b2d929fe588c99114221da_3518.JPG_thumb)
