Question

Y ty=lm I Х 1 x = -2cm 1 x = +2cm Refer to the image above: The current in the long wire located at x=-2cm is increasing linearly at a rate of 100 A/s. The blue triangle is a loop of wire in the shape of a right triangle. (a.) What is the emf induced in the loop of wire? (6.) If the wire forming the loop has a resistance per unit length of 10 Ohms per meter, what is the magnitude and direction of the current flowing in the loop of wire?

Answer 1

Solution 1.050 -501 1 u 2--20m dx 4-2 2-200 According to formula Induced amf & -do at &- flux 0 - 16.dA can see The gnetic field at The so we fake small Here as we magnetic Every point of torangle vary first Send fix for that Integrate H for whole truangle. Element dat and then We and

STAL so after taking Element of Sength da from distance farm were and height y Send flux we for this Nort Magnetic field due to col long wire) at distance from It is B- Mor and 30 Bat this small Element B: Moi ana Now d horough Element d- Bx ds de droex daxy aña 0.02 Py y = 2-2 0.01 002 ya y = 0.2-0.02

dd Mol x &-0.02da daa 2 do= Moi (1-0.02 ) da 4K ·0.04 MOL ЧЛ 0.02/d2 0.02 (do : Moi 0.02 -0.02 02 (0-693)] UK - Lupi [0-02-0 0.01386] 45 o 0.00614 X10-71 W.R:T Time Now Differencate Both Side de 0.00614 X10-7 di at dt Tel 0.00614x10-5 v

JOTAL TESISTANCE 0.01m 0.0201 0.02m Total = length 0.050 lm So Total desistance TOX0.050 1 STED 0.501 ohm Hagnitucle of so cucoon's 9: { R 0-0061-4X10 -7 I - 0.00614 x10-5 0.501 Direction Lenz Law. in 0.0122x100 Amp of current anti-clock wise By is
in this question to find emf i have used formula

e=-$d\theta /dt$

$\theta$=b.ds

and to find direction of current i have used lenz law according to which indused emf oppose its own cause