JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Magnetic Effects of Current

WhatsApp Email

A coil having N turns is would tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil:

(A) $\frac{μ _{0}}{8} [\frac{a + b}{a - b}]$
(B) $\frac{μ _{0} I N}{2 ( b - a )} lo g_{e} (\frac{b}{a})$ ✓ Correct
(C) $\frac{μ _{0} l}{4 ( a - b )} [\frac{1}{a} - \frac{1}{b}]$
(D) $\frac{μ _{0} l}{8} (\frac{a - b}{a + b})$

Answer: (B)

Solution

Divide the spiral into elementary rings. Between radii

a

and

b

the

N

turns are spread uniformly, so a ring of width

d r

at radius

r

carries

d N = \frac{N}{b - a} d r

turns. Its field at the centre is

d B = \frac{μ _{0} I d N}{2 r} = \frac{μ _{0} I N}{2 ( b - a )} \frac{d r}{r}

. Integrating from

a

b

B = \frac{μ _{0} I N}{2 ( b - a )} \int_{a}^{b} \frac{d r}{r} = \frac{μ _{0} I N}{2 ( b - a )} ln \frac{b}{a} .

The field at the centre is

\frac{μ _{0} I N}{2 ( b - a )} lo g_{e} \frac{b}{a}

JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Magnetic Effects of Current →

JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Magnetic Effects of Current

Solution

More JEE Main questions on Magnetic Effects of Current