JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Magnetic Effects of Current

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B_{X}

and

B_{Y}

are the magnetic field at the centre of two coils X and Y respectively, each carrying equal current. If coil X has 200 turns and 20 cm radius and coil Y has 400 turns and 20 cm radius, the ratio of

B_{X}

and

B_{Y}

(A) $1 : 1$
(B) $1 : 2$ ✓ Correct
(C) $2 : 1$
(D) $4 : 1$

Answer: (B)

Solution

Magnetic field at the center of a coil is

B = N \frac{μ _{0} i}{2 R}

.

For coil X:

B_{X} = 200 \times \frac{μ _{0} i}{2 \times 0.2}

For coil Y:

B_{Y} = 400 \times \frac{μ _{0} i}{2 \times 0.2}

Therefore

\frac{B _{X}}{B _{Y}} = \frac{200}{400} = \frac{1}{2}

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Single correct option

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