The intensity of magnetic induction at the centre of a current-carrying circular coil is $B_{1}$ and at a point on its axis at a distance equal to its radius from the centre is $B_{2}$ , then $\frac{B_{1}}{B_{2}}$ is

2 \sqrt{2}

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\frac{1}{2 \sqrt{2}}

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\frac{1}{\sqrt{2}}

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\sqrt{2}

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Solution

The correct option is A $2 \sqrt{2}$
$B_{1} = \frac{μ_{0} i}{2 a}$
$B_{2} = \frac{μ_{0} \cdot i \cdot a^{2}}{2 (a^{2} + a^{2})^{3 / 2}}$
$= \frac{μ_{0} i a^{2}}{2 \times 2 \sqrt{2} \times a^{3}}$
$= \frac{μ_{0} i}{4 \sqrt{2} \times a}$
$\frac{B_{1}}{B_{2}} = 2 \sqrt{2}$

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The intensity of magnetic induction at the centre of a current-carrying circular coil is B1 and at a point on its axis at a distance equal to its radius from the centre is B2, then B1B2 is

The correct option is A 2√2B1=μ0i2aB2=μ0⋅i⋅a22(a2+a2)3/2=μ0ia22×2√2×a3=μ0i4√2×aB1B2=2√2

The intensity of magnetic induction at the centre of a current-carrying circular coil is $B_{1}$ and at a point on its axis at a distance equal to its radius from the centre is $B_{2}$ , then $\frac{B_{1}}{B_{2}}$ is

The correct option is A $2 \sqrt{2}$
$B_{1} = \frac{μ_{0} i}{2 a}$
$B_{2} = \frac{μ_{0} \cdot i \cdot a^{2}}{2 (a^{2} + a^{2})^{3 / 2}}$
$= \frac{μ_{0} i a^{2}}{2 \times 2 \sqrt{2} \times a^{3}}$
$= \frac{μ_{0} i}{4 \sqrt{2} \times a}$
$\frac{B_{1}}{B_{2}} = 2 \sqrt{2}$