JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Magnetic Effects of Current

The ratio of magnetic field at the centre of a current carrying coil of radius

r

to the magnetic field at distance

r

from the centre of coil on its axis is

x : 1

. The value of x is

____

Answer: 8

Solution

Magnetic field at the center of a circular coil:

B_{1} = \frac{μ _{0} I}{2 r}

Magnetic field on the axis at distance

d = r

from the center:

B_{2} = \frac{μ _{0} I r ^{2}}{2 ( r ^{2} + d ^{2} ) ^{3/2}} = \frac{μ _{0} I r ^{2}}{2 ( r ^{2} + r ^{2} ) ^{3/2}} = \frac{μ _{0} I r ^{2}}{2 ( 2 r ^{2} ) ^{3/2}} = \frac{μ _{0} I}{4 2 r}

Ratio:

\frac{B _{1}}{B _{2}} = \frac{μ _{0} I}{2 r} \times \frac{4 2 r}{μ _{0} I} = 22 = 8

Therefore,

x = 8

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Integer answer

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