MHT CET 2021 Physics Solved Paper

(b) According to the question,
Magnetic field at centre of coil A= Magnetic field at centre of coilB
‌

µ0l1

2(2r)

‌‌=‌

µ0l2

2r

⇒‌‌‌

l1

l2

‌‌=2‌‌‌.......(i)
We know, R=ρ(‌

l

A

), where ρ is resistivity, l is length
and A is area of cross-section.
⇒l1=‌

V1

R1

=‌

V1

ρ(‌ l1 A )

⇒‌

V1

l1

=ρ⋅‌

l1

A

‌‌‌.......(ii)
‌ and ‌‌l2=‌

V2

R2

=‌

V2

ρ⋅(‌ l2 A )

⇒‌

V2

l2

=ρ⋅‌

l2

A

‌‌‌......(iii)
From Eqs. (ii) and (iii), we get
‌‌

V1

l1

×‌

l2

V2

=‌

l1

l2

=‌

2πr1

2πr2

⇒‌‌‌

V1

V2

⋅‌

l2

l1

=‌

r1

r2

⇒‌

V1

V2

⋅‌

l2

l1

=‌

2r

r

⇒‌

V1

V2

=2‌

2

l2

=2×2‌‌‌ [from Eq. (i)] ‌
⇒‌‌‌

V1

V2

=‌

4

1

=4:1