JEE Mains 2020 Model Paper 6 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 ϕB B through the loop can be obtained by summing over contributions from all differential are elements dA=ldr.
So, ϕB=∫dϕB=∫

→

B

.d

→

A

=

µ0II

2π

‌

s+w

∫

s

dr

r

=

µ0II

2π

loge(

s+w

s

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

dϕB

dt

=

d

dt

[

µ0II

2π

loge(

s+w

s

)]
=

µ0l

2π

loge(

s+w

s

)

dI

dt

I=I(t)=a+bt⇒

dI

dt

=b
⇒ξ=

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.