Question

Calculate the magnetic field at the center of a circular current loop of radius R divided by the magnetic field at a distance R away from a very long straight wire carrying the same current value I. (Note the loop and wire are not in electrical contact.)

Answer 1

Answer:

The magnetic field at the center of a circular current loop of radius R divided by the magnetic field at a distance R away from a very long straight wire carrying the same current value I is $\pi$ or 3.14

Explanation:

The magnetic field at center of a circular loop is given by

$B = \frac{\mu _{o}I }{2R}$

Where B is the magnetic field

$\mu _{o}$ is the free space permeability constant ( $\mu _{o}$ = 4π × 10⁻⁷ N/A²)

$I$ is the current

and $R$ is the radius

For the magnetic field of a long straight wire, it is given by

$B = \frac{\mu _{o}I }{2\pi R}$

Where B is the magnetic field

$\mu _{o}$ is the free space permeability constant ( $\mu _{o}$ = 4π × 10⁻⁷ N/A²)

$I$ is the current

and $R$ is the distance from the wire

Then, to calculate the magnetic field at the center of a circular current loop of radius R divided by the magnetic field at a distance R away from a very long straight wire carrying the same current value I, that will be

$\frac{\mu _{o}I }{2R} \div \frac{\mu _{o}I }{2\pi R}$

= $\frac{\mu _{o}I }{2R} \times \frac{2\pi R }{\mu _{o}I}$

= $\pi$

(NOTE: $\pi$ = 3.14)

Hence, the magnetic field at the center of a circular current loop of radius R divided by the magnetic field at a distance R away from a very long straight wire carrying the same current value I is $\pi$ or 3.14.