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.)

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 or 3.14

Explanation:

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

Where B is the magnetic field

is the free space permeability constant ( = 4π × 10⁻⁷ N/A²)

is the current

and is the radius

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

Where B is the magnetic field

is the free space permeability constant ( = 4π × 10⁻⁷ N/A²)

is the current

and 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

=

=

(NOTE: = 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 or 3.14.

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