MHT CET · Physics · Magnetic Effects of Current

A circular coil carrying current $I$ has a radius $R$ and magnetic field at the centre is $B$ . The distance from the centre along the axis of the same coil where the magnetic field will be $\frac{B}{8}$ is

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

Verified Solution

Answer & Solution

Correct Answer

(B) $R \sqrt{3}$

Step-by-step Solution

Detailed explanation

B_{center} = \frac{μ_{0} nI}{2 R} = B

B_{x} = \frac{B}{8} = \frac{μ_{0} {nIR}^{2}}{2 {(R^{2} + x^{2})}^{3 / 2}}

\frac{1}{8} (\frac{μ_{0} nI}{2 R}) = \frac{μ_{0} {nIR}^{2}}{2 {(R^{2} + x^{2})}^{3 / 2}}

\frac{1}{8 R^{3}} = \frac{1}{{(R^{2} + x^{2})}^{3 / 2}}

\frac{1}{2 R} = \frac{1}{{(R^{2} + x^{2})}^{\frac{1}{2}}}

4 R^{2} = R^{2} + x^{2}

x^{2} = 3 R^{2}

x = \sqrt{3} R

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A circular coil carrying current I has a radius R and magnetic field at the centre is B. The distance from the centre along the axis of the same coil where the magnetic field will be B8 is

Step-by-step Solution

A circular coil carrying current $I$ has a radius $R$ and magnetic field at the centre is $B$ . The distance from the centre along the axis of the same coil where the magnetic field will be $\frac{B}{8}$ is