JEE Mains 2020 Model Paper 4 New Pattern

For calculating the induced e.m.f. we must first calculate the flux associated with the loop due to field of current carrying wire. The magnetic field due to a current – carrying wire at a distance r away is B = µ0I/2πr. The total magnetic flux ϕp through the loop ca n be obtained by summingover contributions from all differential are elements dA = ldr .
So , ϕB = ∫dϕB = ∫

→

B

.d

→

A

=

µ0II

2π

‌

s+w

∫

s

dr

r

=

µ0II

2π

‌log(

s+w

s

)
According to Faraday’s Law, the induced emf is
ε =

dϕB

dt

=

d

dt

[

µ0II

2π

loge(

s+w

s

)] =

µ0I

2π

loge(

s+w

s

)

dI

dt

I = I (t) = a + bt ⇒

dI

dt

= b ⇒ ε =

µ0bl

2π

loge(

s+w

s

)
The straight wire carrying a current I produces a magnetic flux into the page through the rectangular loop. By Lenz’s Law, the induced current in the loop must be flowing counter clockwise in order to produce a magnetic field out of the page to counteract the increase in inward flux.