Question

A circular coil carrying current 'I' has radius 'R' and magnetic field at the centre is 'B'. At what distance from the centre along the axis of the magnetic field will be `"B"/8`?

Options

• R`sqrt2`

• R`sqrt3`

• 2R

• 3R

Answer 1

R`bbsqrt3`

Explanation:

`"B"_"centre"=(mu_0eta"I")/"R"`

Let at a distance x from the centre, magnetic field becomes `"B"/8`

`"B"/8=(mu_0eta"IR"^2)/(("R"^2+x^2)3//2)`

⇒ `(mu_0eta"I")/(8"R")=(mu_0eta"IR"^2)/(("R"^2+x^2)3//2)`

or, 8R³ = (R² + x²)^3/2

⇒ 2R = (R² + x²)^1/2

or 4R² = R² + x²  [from squaring both sides of equation (i)]

⇒ 3R² = x²

∴ x = `sqrt(3"R"^2) = sqrt3` R