JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Magnetic Effects of Current

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Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of

\frac{μ _{0} I}{π}

is:

(A) $5003$ ✓ Correct
(B) $503$
(C) $53$
(D) $2503$

Answer: (A)

Solution

Each straight side of the coil produces a field at the centre of

\frac{μ _{0} I}{4 π d} (sin 3 0^{\circ} + sin 3 0^{\circ}) = \frac{μ _{0} I}{4 π d}

, where

d = \frac{a 3}{2}

is the perpendicular distance from the centre to a side. Summing over all six sides and

50

turns,

B = 6 \times 50 \times \frac{μ _{0} I}{4 π d} = \frac{300 μ _{0} I}{2 π a 3}

. With

a = 0.1

m this equals

\frac{μ _{0} I}{π} \times 5003

, so in the stated units the magnitude is

5003

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Single correct option

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