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JIPMER 2016

Exam: JIPMER
Year: 2016
Subject: Physics
Chapter: Magnetic Effects of Current

JIPMER 2016 · Physics · Magnetic Effects of Current

A circular current carrying coil has a radius R . The distance from...

A circular current carrying coil has a radius

R

. The distance from the centre of the coil, on the axis, where

B

will be

\frac{1}{8}

of its value at the centre of the coil is

Options

A $\frac{R}{\sqrt{3}}$
B $\sqrt{3} R$
C $2 \sqrt{3} R$
D $\frac{2 R}{\sqrt{3}}$

Correct answer

B. $\sqrt{3} R$

Step-by-step solution

B=\frac{\mu_0 N i R^2}{2\left(R^2+x^2\right)^{3 / 2}}

\begin{aligned} & =\frac{\mu_0 N i}{2 R} \cdot \frac{1}{\left[1+\frac{x^2}{R^2}\right]^{3 / 2}} \\ & =B_C \cdot \frac{1}{\left(1+\frac{x^2}{R^2}\right)^{3 / 2}} \quad\left[\text{ Let } B_C=\frac{\mu_0 N i}{2 R}\right]\end{aligned}

\Rightarrow \quad \frac{B_C}{8}=\frac{B_C}{\left(1+\frac{x^2}{R^2}\right)^{3 / 2}} \quad\left[\because B=\frac{B_C}{8}\right]

\begin{array}{rlrl}\Rightarrow & \left(1+\frac{x^2}{R^2}\right)^{3 / 2} & =8 \\ \Rightarrow & 1+\frac{x^2}{R^2} & =4 \\ \Rightarrow & \frac{x^2}{R^2} & =3 \\ & \therefore & x & =R \sqrt{3}\end{array}

$$

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