JEE Main 27-Aug-2021 Shift 1 Solved Paper

Length of conducting wire, l = 24 a
Resistance of wire is R.
Ratio of magnetic moment of coil for equilateral triangle to square is 1:√y.
Side of equilateral triangle is a and also side of square is a.
Number of turns in equilateral triangle will be
nT=

24a

3a

=8 [ ∵ Length of one turn is 3a]
Number of turns in square will be
nS=

24a

4a

=6 [ ∵ Length of one turn is 4a]
Magnetic moment of coil is given as
M = nIA
The ratio of magnetic moment for triangular coil to square coil is given as

MT

MS

=

nTIAT

nSIAS

(∵ I is same in both coils)
Substituting the values in above expression, we get

1

√y

=

(8× √3 4 a2)

6×a2

=

8√3

24

=

1

√3

⇒√y=√3
⇒ y = 3
Hence, the value of y is 3.