JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Magnetic Effects of Current

One of the two identical conducing wires of length

L

is bent in the form of a circular loop and the other one into a circular coil of

N

identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop

(B_{L})

to that at the centre of the coil

(B_{C})

, i.e.

\frac{B _{L}}{B _{C}}

will be

Answer: (D)

Solution

Both wires have the same length

L

. Bent into a single loop, the radius is

R = \frac{L}{2 π}

and the central field is

B_{L} = \frac{μ _{0} i}{2 R} = \frac{μ _{0} iπ}{L}

. Wound into

N

turns, each turn has circumference

\frac{L}{N}

, so radius

r = \frac{L}{2 π N}

, and the

N

turns together give

B_{C} = \frac{μ _{0} N i}{2 r} = \frac{μ _{0} iπ N ^{2}}{L}

. Dividing one by the other,

\frac{B _{L}}{B _{C}} = \frac{1}{N ^{2}}

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Single correct option