Question

The ratio of magnetic field and magnetic moment at the centre of a current carrying circular loop is x. When both the current and radius is doubled then the ratio will be ______.

Options

• `x/8`

• `x/4`

• `x/2`

• 2x

Answer 1

The ratio of magnetic field and magnetic moment at the centre of a current carrying circular loop is x. When both the current and radius is doubled then the ratio will be `x/8`

Explanation:

Magnetic field at the centre of a circular loop of radius R carrying current I,

`"B"= (µ_0 2π"I")/(4π"R")=(µ_0"I")/2"R" and "M"="IA"="I"(π"R"^2)`

∴ `"B"/"M"= (µ_0"I")/(2"R")=(1)/("I"π"R"^2) = µ_0/(2π"R"^3)="x"` [Given]

When both the current and radius are doubled, the ratio becomes

`"B'"/"M'"=µ_0/(2π(2R)^3) =1/8(µ_0/(2πR^3))="X"/8`