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 `bbunderline(x/8)`

Explanation:

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

`B= (µ_0 2πI)/(4πR)` 

= `(µ_0I)/2R` 

M = IA

= I(πR²)

∴ `B/M= (µ_0I)/(2R)`

= `(1)/(IπR^2)`

= `µ_0/(2πR^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`