The fractional change in the magnetic field intensity at a distance ‘r’ from centre on the axis of current carrying coil of radius ‘a’ to the magnetic field intensity at the centre of the same coil is: (Take r < a)

Option 1 -

$\frac{2}{3} \frac{a^{2}}{r^{2}}$

Option 2 -

$\frac{2}{3} \frac{r^{2}}{a^{2}}$

Option 3 -

$\frac{3}{2} \frac{a^{2}}{r^{2}}$

Option 4 -

$\frac{3}{2} \frac{r^{2}}{a^{2}}$

2 Views | Posted 4 months ago

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

4 months ago

Correct Option - 4

Detailed Solution:

$B_{a x i s} = \frac{μ_{0} N l a^{2}}{2 {(a^{2} + r^{2})}^{3 / 2}}$

$B_{c e n t} = \frac{μ_{0} N I}{2 a}$

Fractional change = $\frac{B_{c e n t r e} - B_{a x i s}}{B_{c e n t r e}}$

$= 1 - \frac{B_{a x i s}}{B_{c e n t r e}}$

$= 1 - (1 - \frac{3 r^{2}}{2 a^{2}}) [r < < a]$

$= \frac{3 r^{2}}{2 a^{2}}$

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The fractional change in the magnetic field intensity at a distance ‘r’ from centre on the axis of current carrying coil of radius ‘a’ to the magnetic field intensity at the centre of the same coil is: (Take r < a)

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