5.0-A current. (a) Find the magnetic field at a point along the axis of the coil, 0.80 m from the center. (b) Along the axis, at what distance from the center of the coil is the field magnitude 1 8 as great as it is at the center

Here is the full question

A coil consisting of 100  circular loops with radius 0.6 m carries a 5.0-A current.

(a) Find the magnetic field at a point along the axis of the coil, 0.80 m from the center.

(b) Along the axis, at what distance from the center of the coil is the field magnitude 1/8 as great as it is at the center

a) B = 0.000113 T

b) The distance (x) from the center of the coil = 1.038 m

Explanation:

The formula for the magnetic field on the line of axis of the circular loop can be expressed as:

B =

where;

N = number of turns = 100

I = current flowing through the coil = 5.0- A

r = radius of the circular loop = 0.6 m

x = distance from the center of the coil

So;

B = 0.000113 T

b)

Also; to determine the distance (x) from the center of the coil; we have the following:

We know that the magnetic field at the center of the coil can be expressed as:

Now; given that the field magnitude is 1/8 as great as it is at the center; Then ;

∴

=

Therefore, the distance from the center of the coil is  = 1.038 m